- Worksheet on Frequency Distribution
In worksheet on frequency distribution the questions are based on arranging data in ascending order or descending order and constructing the frequency distribution table.
1. Arrange the following data in ascending order.
(a) 7, 2, 10, 14, 0, 6, 15, 24, 8, 3
(b) 4.6, 8.1, 2.0, 3.5, 0.7, 9.3, 1.4, 0.8
2. Arrange the following data in descending order.
(a) 14, 2, 0, 10, 6, 1, 22, 13, 28, 4, 8, 16
(b) 1.2, 3.5, 0.1, 0.3, 2.4, 8.6, 5.0, 3.7, 0.7, 0.9
3. Construct the frequency table for each of the following.
(a) 4, 3, 6, 5, 2, 4, 3, 3, 6, 4, 2, 3, 2, 2, 3, 3, 4, 5, 6, 4, 2, 3, 4
(b) 6, 7, 5, 4, 5, 6, 6, 8, 7, 9, 6, 5, 6, 7, 7, 8, 9, 4, 6, 7, 6, 5
4. The marks obtained out of 25 by 30 students of a class in the examination are given below.
20, 6, 23, 19, 9, 14, 15, 3, 1, 12, 10, 20, 13, 3, 17, 10, 11, 6, 21, 9, 6, 10, 9, 4, 5, 1, 5, 11, 7, 24
Represent the above data as a grouped data taking the class interval 0 - 5
5. Complete the table given below.
6. Weekly pocket expenses (in $) of 30 students of class VIII are 37, 41, 39, 34, 71, 26, 56, 61, 58, 79, 83, 72, 64, 39, 75, 39, 37, 59, 57, 37, 53, 38, 49, 45, 70, 82, 44, 37, 79, 76.
Construct the grouped frequency table with the class interval of equal width such as 30 - 35. Also, find the range of the weekly pocket expenses.
7. Pulse rate (per minute) of 25 persons were recorded as
Construct a frequency table expressing the data in the inclusive form taking the class interval 61-65 of equal width. Now, convert this data again into the exclusive form in the separate table.
8. The frequency distribution of weights (in kg) of 40 persons is given below.
(a) What is the lower limit of fourth class interval?
(b) What is the class size of each class interval?
(c ) Which class interval has the highest frequency?
(d) Find the class marks of all the class intervals?
9. Construct the frequency distribution table for the data on heights (cm) of 20 boys using the class intervals 130 - 135, 135 - 140 and so on. The heights of the boys in cm are: 140, 138, 133, 148, 160, 153, 131, 146, 134, 136, 149, 141, 155, 149, 165, 142, 144, 147, 138, 139. Also, find the range of heights of the boys.
10. Construct a frequency distribution table for the following weights (in gm) of 30 oranges using the equal class intervals, one of them is 40-45 (45 not included). The weights are: 31, 41, 46, 33, 44, 51, 56, 63, 71, 71, 62, 63, 54, 53, 51, 43, 36, 38, 54, 56, 66, 71, 74, 75, 46, 47, 59, 60, 61, 63.
(a) What is the class mark of the class intervals 50-55?
(b) What is the range of the above weights?
(c) How many class intervals are there?
(d) Which class interval has the lowest frequency?
Answers for worksheet on frequency distribution are given below to check the exact answers of the above questions on presentation data.
1. (a) 0, 2, 3, 6, 7, 8, 10, 14, 15, 24
(b) 0.7, 0.8, 1.4, 2.0, 3.5, 4.6, 8.1, 9.3
2. (a) 28, 22, 16, 14, 13, 10, 8, 6, 4, 2, 0, 1
(b) 8.6, 5.0, 3.7, 3.5, 2.4, 1.2, 0.9, 0.7, 0.3, 0.1
(d) 32.5, 37.5, 42.5, 47.5, 52.5
Range = 34 cm
(d) 65 - 70, 75 - 80
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- Frequency Distribution | Tables, Types & Examples
Frequency Distribution | Tables, Types & Examples
Published on June 7, 2022 by Shaun Turney . Revised on June 21, 2023.
A frequency distribution describes the number of observations for each possible value of a variable . Frequency distributions are depicted using graphs and frequency tables.
Table of contents
What is a frequency distribution, how to make a frequency table, how to graph a frequency distribution, other interesting articles, frequently asked questions about frequency distributions.
The frequency of a value is the number of times it occurs in a dataset. A frequency distribution is the pattern of frequencies of a variable. It’s the number of times each possible value of a variable occurs in a dataset.
Types of frequency distributions
There are four types of frequency distributions:
- You can use this type of frequency distribution for categorical variables .
- You can use this type of frequency distribution for quantitative variables .
- You can use this type of frequency distribution for any type of variable when you’re more interested in comparing frequencies than the actual number of observations.
- You can use this type of frequency distribution for ordinal or quantitative variables when you want to understand how often observations fall below certain values .
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Frequency distributions are often displayed using frequency tables . A frequency table is an effective way to summarize or organize a dataset. It’s usually composed of two columns:
- The values or class intervals
- Their frequencies
The method for making a frequency table differs between the four types of frequency distributions. You can follow the guides below or use software such as Excel, SPSS, or R to make a frequency table.
How to make an ungrouped frequency table
- For ordinal variables , the values should be ordered from smallest to largest in the table rows.
- For nominal variables , the values can be in any order in the table. You may wish to order them alphabetically or in some other logical order.
- Especially if your dataset is large, it may help to count the frequencies by tallying . Add a third column called “Tally.” As you read the observations, make a tick mark in the appropriate row of the tally column for each observation. Count the tally marks to determine the frequency.
How to make a grouped frequency table
- Calculate the range . Subtract the lowest value in the dataset from the highest.
- Create a table with two columns and as many rows as there are class intervals. Label the first column using the variable name and label the second column “Frequency.” Enter the class intervals in the first column.
- Count the frequencies. The frequencies are the number of observations in each class interval. You can count by tallying if you find it helpful. Enter the frequencies in the second column of the table beside their corresponding class intervals.
Round the class interval width to 10.
The class intervals are 19 ≤ a < 29, 29 ≤ a < 39, 39 ≤ a < 49, 49 ≤ a < 59, and 59 ≤ a < 69.
How to make a relative frequency table
- Create an ungrouped or grouped frequency table .
- Add a third column to the table for the relative frequencies. To calculate the relative frequencies, divide each frequency by the sample size. The sample size is the sum of the frequencies.
How to make a cumulative frequency table
- Create an ungrouped or grouped frequency table for an ordinal or quantitative variable. Cumulative frequencies don’t make sense for nominal variables because the values have no order—one value isn’t more than or less than another value.
- Add a third column to the table for the cumulative frequencies. The cumulative frequency is the number of observations less than or equal to a certain value or class interval. To calculate the relative frequencies, add each frequency to the frequencies in the previous rows.
- Optional: If you want to calculate the cumulative relative frequency , add another column and divide each cumulative frequency by the sample size.
Pie charts, bar charts, and histograms are all ways of graphing frequency distributions. The best choice depends on the type of variable and what you’re trying to communicate.
A pie chart is a graph that shows the relative frequency distribution of a nominal variable .
A pie chart is a circle that’s divided into one slice for each value. The size of the slices shows their relative frequency.
This type of graph can be a good choice when you want to emphasize that one variable is especially frequent or infrequent, or you want to present the overall composition of a variable.
A disadvantage of pie charts is that it’s difficult to see small differences between frequencies. As a result, it’s also not a good option if you want to compare the frequencies of different values.
A bar chart is a graph that shows the frequency or relative frequency distribution of a categorical variable (nominal or ordinal).
The y -axis of the bars shows the frequencies or relative frequencies, and the x -axis shows the values. Each value is represented by a bar, and the length or height of the bar shows the frequency of the value.
A bar chart is a good choice when you want to compare the frequencies of different values. It’s much easier to compare the heights of bars than the angles of pie chart slices.
A histogram is a graph that shows the frequency or relative frequency distribution of a quantitative variable . It looks similar to a bar chart.
The continuous variable is grouped into interval classes , just like a grouped frequency table . The y -axis of the bars shows the frequencies or relative frequencies, and the x -axis shows the interval classes. Each interval class is represented by a bar, and the height of the bar shows the frequency or relative frequency of the interval class.
Although bar charts and histograms are similar, there are important differences:
A histogram is an effective visual summary of several important characteristics of a variable. At a glance, you can see a variable’s central tendency and variability , as well as what probability distribution it appears to follow, such as a normal , Poisson , or uniform distribution.
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
- Student’s t table
- Student’s t distribution
- Quartiles & Quantiles
- Measures of central tendency
- Correlation coefficient
Methodology
- Cluster sampling
- Stratified sampling
- Types of interviews
- Cohort study
- Thematic analysis
Research bias
- Implicit bias
- Cognitive bias
- Survivorship bias
- Availability heuristic
- Nonresponse bias
- Regression to the mean
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A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution .
Plot a histogram and look at the shape of the bars. If the bars roughly follow a symmetrical bell or hill shape, like the example below, then the distribution is approximately normally distributed.
Categorical variables can be described by a frequency distribution. Quantitative variables can also be described by a frequency distribution, but first they need to be grouped into interval classes .
Probability is the relative frequency over an infinite number of trials.
For example, the probability of a coin landing on heads is .5, meaning that if you flip the coin an infinite number of times, it will land on heads half the time.
Since doing something an infinite number of times is impossible, relative frequency is often used as an estimate of probability. If you flip a coin 1000 times and get 507 heads, the relative frequency, .507, is a good estimate of the probability.
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Frequency Distribution
A frequency distribution shows the frequency of repeated items in a graphical form or tabular form. It gives a visual display of the frequency of items or shows the number of times they occurred. Let's learn about frequency distribution in this article in detail.
What is Frequency Distribution?
Frequency distribution is used to organize the collected data in table form. The data could be marks scored by students, temperatures of different towns, points scored in a volleyball match, etc. After data collection, we have to show data in a meaningful manner for better understanding. Organize the data in such a way that all its features are summarized in a table. This is known as frequency distribution.
Let's consider an example to understand this better. The following are the scores of 10 students in the G.K. quiz released by Mr. Chris 15, 17, 20, 15, 20, 17, 17, 14, 14, 20. Let's represent this data in frequency distribution and find out the number of students who got the same marks.
We can see that all the collected data is organized under the column quiz marks and the number of students. This makes it easier to understand the given information and we can see that the number of students who obtained the same marks. Thus, frequency distribution in statistics helps us to organize the data in an easy way to understand its features at a glance.
Frequency Distribution Graphs
There is another way to show data that is in the form of graphs and it can be done by using a frequency distribution graph. The graphs help us to understand the collected data in an easy way. The graphical representation of a frequency distribution can be shown using the following:
- Bar Graphs : Bar graphs represent data using rectangular bars of uniform width along with equal spacing between the rectangular bars.
- Histograms : A histogram is a graphical presentation of data using rectangular bars of different heights. In a histogram, there is no space between the rectangular bars.
- Pie Chart : A pie chart is a type of graph that visually displays data in a circular chart. It records data in a circular manner and then it is further divided into sectors that show a particular part of data out of the whole part.
- Frequency Polygon: A frequency polygon is drawn by joining the mid-points of the bars in a histogram.
Types of Frequency Distribution
There are four types of frequency distribution under statistics which are explained below:
- Ungrouped frequency distribution: It shows the frequency of an item in each separate data value rather than groups of data values.
- Grouped frequency distribution: In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.
- Relative frequency distribution: It tells the proportion of the total number of observations associated with each category.
- Cumulative frequency distribution: It is the sum of the first frequency and all frequencies below it in a frequency distribution. You have to add a value with the next value then add the sum with the next value again and so on till the last. The last cumulative frequency will be the total sum of all frequencies.
- Frequency Distribution Table
A frequency distribution table is a chart that shows the frequency of each of the items in a data set. Let's consider an example to understand how to make a frequency distribution table using tally marks. A jar containing beads of different colors- red, green, blue, black, red, green, blue, yellow, red, red, green, green, green, yellow, red, green, yellow. To know the exact number of beads of each particular color, we need to classify the beads into categories. An easy way to find the number of beads of each color is to use tally marks . Pick the beads one by one and enter the tally marks in the respective row and column. Then, indicate the frequency for each item in the table.
Thus, the table so obtained is called a frequency distribution table .
Types of Frequency Distribution Table
There are two types of frequency distribution tables: Grouped and ungrouped frequency distribution tables.
Grouped Frequency Distribution Table: To arrange a large number of observations or data, we use grouped frequency distribution table. In this, we form class intervals to tally the frequency for the data that belongs to that particular class interval.
For example, Marks obtained by 20 students in the test are as follows. 5, 10, 20, 15, 5, 20, 20, 15, 15, 15, 10, 10, 10, 20, 15, 5, 18, 18, 18, 18. To arrange the data in grouped table we have to make class intervals. Thus, we will make class intervals of marks like 0 – 5, 6 – 10, and so on. Given below table shows two columns one is of class intervals (marks obtained in test) and the second is of frequency (no. of students). In this, we have not used tally marks as we counted the marks directly.
Ungrouped Frequency Distribution Table: In the ungrouped frequency distribution table, we don't make class intervals, we write the accurate frequency of individual data. Considering the above example, the ungrouped table will be like this. Given below table shows two columns: one is of marks obtained in the test and the second is of frequency (no. of students).
Important Notes:
Following are the important points related to frequency distribution.
- Figures or numbers collected for some definite purpose is called data.
- Frequency is the value in numbers that shows how often a particular item occurs in the given data set.
- There are two types of frequency table - Grouped Frequency Distribution and Ungrouped Frequency Distribution.
- Data can be shown using graphs like histograms, bar graphs, frequency polygons, and so on.
Related Articles on Frequency Distribution
To learn more about the frequency distribution, check the given articles.
- Data Handling
Frequency Distribution Examples
Example 1: There are 20 students in a class. The teacher, Ms. Jolly, asked the students to tell their favorite subject. The results are as follows - Mathematics, English, Science, Science, Mathematics, Science, English, Art, Mathematics, Mathematics, Science, Art, Art, Science, Mathematics, Art, Mathematics, English, English, Mathematics.
Represent this data in the form of frequency distribution and identify the most-liked subject?
Solution: 20 students have indicated their choices of preferred subjects. Let us represent this data using tally marks. The tally marks are showing the frequency of each subject.
According to the above frequency distribution, mathematics is the most liked subject.
Example 2: 100 schools decided to plant 100 tree saplings in their gardens on world environment day. Represent the given data in the form of frequency distribution and find the number of schools that are able to plant 50% of the plants or more? 95, 67, 28, 32, 65, 65, 69, 33, 98, 96, 76, 42, 32, 38, 42, 40, 40, 69, 95, 92, 75, 83, 76, 83, 85, 62, 37, 65, 63, 42, 89, 65, 73, 81, 49, 52, 64, 76, 83, 92, 93, 68, 52, 79, 81, 83, 59, 82, 75, 82, 86, 90, 44, 62, 31, 36, 38, 42, 39, 83, 87, 56, 58, 23, 35, 76, 83, 85, 30, 68, 69, 83, 86, 43, 45, 39, 83, 75, 66, 83, 92, 75, 89, 66, 91, 27, 88, 89, 93, 42, 53, 69, 90, 55, 66, 49, 52, 83, 34, 36
Solution: To include all the observations in groups, we will create various groups of equal intervals. These intervals are called class intervals. In the frequency distribution, the number of plants survived is showing the class intervals, tally marks are showing frequency, and the number of schools is the frequency in numbers.
So, according to class intervals starting from 50 – 59 to 90 – 99, the frequency of schools able to retain 50% or more plants are 8 + 18 + 10 + 23 + 12 = 71 schools. Thus, 71 schools are able to retain 50% or more plants in their garden.
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Frequency Distribution Practice Questions
Faqs on frequency distribution, what is a frequency distribution in math.
In statistics, the frequency distribution is a graph or data set organized to represent the frequency of occurrence of each possible outcome of an event that is observed a specific number of times. Frequency distribution is a tabular or graphical representation of the data that shows the frequency of all the observations.
What are the 2 Types of Frequency Distribution Table?
The 2 types of frequency distributions are:
- Ungrouped frequency distribution
- Grouped frequency distribution
Why are Frequency Distributions Important?
Frequency charts are the best way to organize data. Doctors use it to understand the frequency of diseases. Sports analysts use it to understand the performance of a sportsperson. Wherever you have a large amount of data, frequency distribution makes it easy to analyze the data.
How do you find Frequency Distribution?
Follow the steps to find frequency distribution:
- Step 1: To make a frequency chart, first, write the categories in the first column.
- Step 2: In the next step, tally the score in the second column.
- Step 3: And finally, count the tally to write the frequency of each category in the third column.
Thus, in this way, we can find the frequency distribution of an event.
What is the Difference Between Frequency Table and Frequency Distribution?
The frequency table is a tabular method where the frequency is assigned to its respective category. Whereas, a frequency distribution is known as the graphical representation of the frequency table.
What is Grouped Frequency Distribution?
A grouped frequency distribution shows the scores by grouping the observations into intervals and then lists these intervals in the frequency distribution table. The intervals in grouped frequency distribution are called class limits.
What is Ungrouped Frequency Distribution?
The ungrouped frequency distribution is a type of frequency distribution that displays the frequency of each individual data value instead of groups of data values. In this type of frequency distribution, we can directly see how often different values occurred in the table.
What are the Components of Frequency Distribution?
The components of the frequency distribution are as follows:
- Class interval
- Types of class interval
- Class boundaries
- Midpoint or classmark
- Width or size of class interval
- Class frequency
- Frequency class width
Frequency Distribution
Frequency is how often something occurs.
Example: Sam played football on:
- Saturday Morning,
- Saturday Afternoon
- Thursday Afternoon
The frequency was 2 on Saturday, 1 on Thursday and 3 for the whole week.
By counting frequencies we can make a Frequency Distribution table.
Example: Goals
Sam's team has scored the following numbers of goals in recent games
2, 3, 1, 2, 1, 3, 2, 3, 4, 5, 4, 2, 2, 3
Sam put the numbers in order, then added up:
- how often 1 occurs (2 times),
- how often 2 occurs (5 times),
and wrote them down as a Frequency Distribution table.
From the table we can see interesting things such as
- getting 2 goals happens most often
- only once did they get 5 goals
This is the definition:
Frequency Distribution : values and their frequency (how often each value occurs).
Here is another example:
Example: Newspapers
These are the numbers of newspapers sold at a local shop over the last 10 days:
22, 20, 18, 23, 20, 25, 22, 20, 18, 20
Let us count how many of each number there is:
It is also possible to group the values. Here they are grouped in 5s:
(Learn more about Grouped Frequency Distributions )
After creating a Frequency Distribution table you might like to make a Bar Graph or a Pie Chart using the Data Graphs (Bar, Line and Pie) page.
Frequency Distribution Table
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Exercises - Frequency Distributions and Histograms
What is the relative frequency of integers contained in the interval $[171,320]$?
For a frequency distribution for the data above, with 8 classes, find the smallest integer that can be used for the class width.
Construct a frequency distribution with 8 classes, indicating both the class limits and class boundaries. Note, end classes may not be empty. Choose "nice" numbers, to the extent possible.
Construct the histogram that corresponds to frequency distribution constructed in part (c) for this data
For each integer that occurs in the data set, find the number of times it occurs divided by the number of values in the data set. So for example, 186 appears 3 times, and thus has relative frequency of $3/30 = 0.10$.
Note, one can do the counting just suggested by hand -- or much more quickly using the table(data) function in R, which prints how often each value in the vector data occurred.
- Limits Boundaries Frequency 171 - 190 170.5 - 190.5 11 191 - 210 190.5 - 210.5 11 211 - 230 210.5 - 230.5 2 231 - 250 230.5 - 250.5 5 251 - 270 250.5 - 270.5 0 271 - 291 270.5 - 290.5 0 291 - 310 290.5 - 310.5 0 311 - 330 310.5 - 330.5 1
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Worksheets- Introductory Statistics
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The LibreTexts worksheets are documents with questions or exercises for students to complete and record answers and are intended to help a student become proficient in a particular skill that was taught to them in class.
- 1.1.1: Central Limit Theorem- Cookie Recipes (Worksheet) The student will demonstrate and compare properties of the central limit theorem.
- 1.1.2: Central Limit Theorem- Pocket Change (Worksheet) The student will demonstrate and compare properties of the central limit theorem.
- 1.1.3: Chi-Square - Goodness-of-Fit (Worksheet) The student will evaluate data collected to determine if they fit either the uniform or exponential distributions.
- 1.1.4: Chi-Square - Test of Independence (Worksheet) The student will evaluate if there is a significant relationship between favorite type of snack and gender.
- 1.1.5: Confidence Interval- Home Costs (Worksheet) The student will calculate the 90% confidence interval for the mean cost of a home in the area in which this school is located. The student will interpret confidence intervals. The student will determine the effects of changing conditions on the confidence interval.
- 1.1.6: Confidence Interval- Place of Birth (Worksheet) The student will calculate the 90% confidence interval for the mean cost of a home in the area in which this school is located. The student will interpret confidence intervals. The student will determine the effects of changing conditions on the confidence interval.
- 1.1.7: Confidence Interval- Women's Heights (Worksheet) The student will calculate a 90% confidence interval using the given data. The student will determine the relationship between the confidence level and the percentage of constructed intervals that contain the population mean.
- 1.1.8: Continuous Distribution (Worksheet) The student will calculate a 90% confidence interval using the given data. The student will determine the relationship between the confidence level and the percentage of constructed intervals that contain the population mean.
- 1.1.9: Data Collection Experiment (Worksheet) The student will demonstrate the systematic sampling technique. The student will construct relative frequency tables. The student will interpret results and their differences from different data groupings.
- 1.1.10: Descriptive Statistics (Worksheet) The student will construct a histogram and a box plot. The student will calculate univariate statistics. The student will examine the graphs to interpret what the data implies.
- 1.1.11: Discrete Distribution- Lucky Dice Experiment (Worksheet) The student will construct a histogram and a box plot. The student will calculate univariate statistics. The student will examine the graphs to interpret what the data implies.
- 1.1.12: Discrete Distribution- Playing Card Experiment (Worksheet) The student will compare empirical data and a theoretical distribution to determine if an everyday experiment fits a discrete distribution. The student will demonstrate an understanding of long-term probabilities.
- 1.1.13: Hypothesis Testing for Two Means and Two Proportions (Worksheet) The student will select the appropriate distributions to use in each case. The student will conduct hypothesis tests and interpret the results.
- 1.1.14: Hypothesis Testing of a Single Mean and Single Proportion (Worksheet) A statistics Worksheet: The student will select the appropriate distributions to use in each case. The student will conduct hypothesis tests and interpret the results.
- 1.1.15: Normal Distribution- Lap Times (Worksheet) The student will compare and contrast empirical data and a theoretical distribution to determine if Terry Vogel's lap times fit a continuous distribution.
- 1.1.16: Normal Distribution- Pinkie Length (Worksheet) The student will compare empirical data and a theoretical distribution to determine if data from the experiment follow a continuous distribution.
- 1.1.17: One-Way ANOVA (Worksheet) The student will conduct a simple one-way ANOVA test involving three variables
- 1.1.18: Probability Topics (Worksheet) The student will use theoretical and empirical methods to estimate probabilities. The student will appraise the differences between the two estimates. The student will demonstrate an understanding of long-term relative frequencies.
- 1.1.19: Regression- Distance from School (Worksheet) The student will calculate and construct the line of best fit between two variables. The student will evaluate the relationship between two variables to determine if that relationship is significant.
- 1.1.20: Regression- Fuel Efficiency (Worksheet) The student will calculate and construct the line of best fit between two variables. The student will evaluate the relationship between two variables to determine if that relationship is significant.
- 1.1.21: Regression- Textbook Costs (Worksheet) The student will calculate and construct the line of best fit between two variables. The student will evaluate the relationship between two variables to determine if that relationship is significant.
- 1.1.22: Sampling Experiment (Worksheet) The student will demonstrate the simple random, systematic, stratified, and cluster sampling techniques. The student will explain the details of each procedure used.
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Frequency Tables
Frequency Table
Here we will learn about frequency tables, including what a frequency table is and how to make a frequency table. We will also look at how they can be used to help analyse a set of data.
There are also frequency table worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What is a frequency table?
A frequency table is a way of organising collected data.
To do this we draw a table with three columns:
- The first column is for the different items in the data set.
- The second column is for the tally marks.
- The last column is the frequency column where we can add up the tally marks and write in the corresponding frequencies.
We can add up all of the frequencies to find the total frequency of the set of data.
For example,
Organise the colours of the 12 shirts in a wardrobe into a frequency table.
blue pink blue white white blue
black white blue pink blue white
The total number of shirts is 12.
Averages from frequency tables
We use frequency tables to find descriptive statistics. These are values which help describe the set of data such as the mean, median and mode of a set of data.
A frequency table showing the ages of 25 students on a college course.
The mode is 18
The median is the 13^{th} value which is 18
The mean can be calculated using the total of all the values, divided by the total of the frequencies, n.
Step-by-step guide: Averages from a frequency table
See also: Mean from a frequency table and Mode from a frequency table
Grouped frequency table
Numerical data can also be organised into grouped data. Here the data is put into different classes with class intervals.
A grouped frequency table showing the heights of 15 students.
The mode class is 140<h\leq150
The median is the 8^{th} value which is in the 140<h\leq150 class interval
We can only calculate an estimate for the mean using the midpoints of the class intervals. The total of the frequencies is n.
\text{mean}=\frac{\text{total}}{n}=\frac{(135\times 3)+(145\times 7)+(155\times 5)}{15}=\frac{2195}{15}=146.3 (1 d.p.)
Step-by-step guide : Grouped frequency table
See also: Median from a frequency table and Modal class
Frequency tables can be used to draw bar charts, pie charts or histograms. They can also be used to find cumulative frequency which in turn can be used to estimate median values and upper and lower quartiles for grouped data.
How to make and use frequency tables
In order to make and use frequency tables, here are some tips to consider:
- Read the frequency table carefully and check the headings.
- If there are groups, check the beginning and end of the intervals.
- If you are finding an average, check which one you are asked to find.
Explain how to make and use frequency tables
Frequency table worksheet
Get your free frequency table worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Frequency table examples
Example 1: categorical data.
Here are the makes of 20 cars.
Ford BMW Honda Honda VW Toyota
Ford Toyota Honda Toyota Ford Honda
Honda VW Toyota Honda Ford Ford
- Complete the frequency table.
- Go along the data set and for each item put a tally mark in the table. When you have finished, add up the tally marks to find the frequencies.
- Add up the frequencies in the final column to get the total number of items in the data set.
Example 2: numerical data
Here are the temperatures at midday for 7 days (in ०C)
Example 3: grouped data
Here are the speeds of 20 vehicles, to the nearest mph.
- Complete the grouped frequency table:
- Go along the data set and for each item put a tally mark in the table. When you have finished, add up the tally marks to find the frequencies. Take care with the inequalities and the minimum value and the maximum value in each class interval.
Example 4: average from a frequency table
Write down the mode.
- The mode is ‘Car’ as it has the highest frequency. The modal vehicle is ‘Car’.
Example 5: averages from a frequency table
Find the mode, median and mean from this frequency table
- The mode is 20^{\circ}
- The median is the 11^{th} value which is 19^{\circ}
- The mean is \frac{(17\times 1)+(18\times 4)+(19\times 6)+ (20\times 8)+(21\times 2)}{21}=\frac{405}{21}=19.3^{\circ} (1 d.p.)
Example 6: averages from a grouped frequency table
Find the modal class, the class interval in which the median lies and the estimated mean from this grouped frequency table
- The modal class is the one with the highest frequency which is 60 \leq x <70 degrees
- The median will be the 13^{th} value which is in the interval 60 \leq x <70
- An estimate for the mean can be found from using the midpoints. Where n is the total frequency. \text{Mean}=\frac{\text{total}}{n}=\frac{(45times 4)+(55\times 8)+(65\times 10)+ (75\times 3)}{25}=\frac{1495}{25}=59.8 \ \text{mph}
Common misconceptions
- Counting the items
When attempting to count the items in each group and fill in the frequencies it is easy to make a mistake. Using tally marks can help with accuracy.
- Check which average you are being asked for
Check if you have been asked for the median, mode or mean average.
- Classes for grouped frequency tables can be written in different ways
The class intervals used in grouped frequency tables can be written in different ways. Take care with inequalities that the item goes in the correct group, especially the minimum value and the maximum value.
E.g. 0 to 5 0-5 0\le x<5 0<x \le5
Practice frequency table questions
1. Which is the correct frequency table for the following set of data?
golf football hockey athletics football
athletics rugby hockey football rugby
hockey football golf hockey rugby
football hockey rugby football athletics
Athletics occurs 3 times in the data set, football 6 times, golf 2 times, hockey 5 times and rugby 4 times.
2. Which is the correct frequency table for the following set of data?
The number 11 occurs six times in the data set, the number 12 five times, the number 13 two times, the number 14 five times and the number 15 three times.
3. Which is the correct grouped frequency table for the following set of data?
Checking the first group, there are 3 numbers in the 0 to 9 class. Checking the second group, there are 5 numbers in the 10 to 19 class. There are 3 numbers in the 20 to 29 class and 4 numbers in the 30 to 39 class.
4. The frequency table shows the number of passengers for 20 buses. Find the modal class interval of passengers:
‘30 to 44’ is the modal class interval as it has the highest frequency.
5. The frequency table shows the number of siblings for 45 children. Find the median number of siblings:
There are 45 items of data. The middle value will be the 23^{rd} value. This will be ‘1’. So 1 is the median
6. The frequency table shows the heights of 20 shrubs. Find the estimate for mean height:
We need to multiply the heights by their frequencies to get the total.
The estimate of the mean is 46
Frequency table GCSE questions
1. Mrs Smith asked 20 children how they got to school.
Here are the results:
(a) Complete the frequency table.
(b) Write the mode.
For at least one correct tally or frequency
For all frequencies correct
(b) Mode is ‘walk’
2. The price of 1 pint of milk is recorded from 40 different shops.
Here are the results, in a grouped frequency table.
(a) State the mode.
(b) Find the median.
(c) Calculate the mean price.
3. Jai times 23 people on how long it takes for them to complete a wordsearch.
(a) State the modal class interval.
(b) Find the class interval which contains the median.
(c) Calculate an estimate for the mean time.
Give your answer correct to 1 decimal place.
(a) 20<t\leq 30
(b) 10<t\leq 20
5, 15, 25 and 35
For the midpoints
For the dividing the sum of the products by 23
For the correct answer
Learning checklist
You have now learned how to:
- Make frequency tables and grouped frequency tables
- Find averages from frequency table and grouped frequency table
The next lessons are
- Cumulative frequency
- Types of sampling methods
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Construct the frequency distribution table for the data on heights (cm) of 20 boys using the class intervals 130 - 135, 135 - 140 and so on. The heights of the boys in cm are: 140, 138, 133, 148, 160, 153, 131, 146, 134, 136, 149, 141, 155, 149, 165, 142, 144, 147, 138, 139. ... Answers for worksheet on frequency distribution are given below to ...
Frequency Distribution Worksheet Probability & Statistics 1. The number of hours taken by transmission mechanics to remove, repair, and replace ... 5.5 3.3 6.7 8.7 4.1 Construct a frequency distribution with 10 intervals of 1.0 hours from the table of data. If the management believes that more than 6.0 hours is evidence of unsatisfactory ...
A frequency distribution describes the number of observations for each possible value of a variable. Frequency distributions are depicted using graphs and frequency tables. Example: Frequency distribution. In the 2022 Winter Olympics, Team USA won 25 medals. This frequency table gives the medals' values (gold, silver, and bronze) and frequencies:
6. 2. 7. 1. A frequency is the number of times a value of the data occurs. According to Table Table 2.1.1 2.1. 1, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.
Worksheet 3 Note: A pictograph is the representation of data using images. Pictographs represent the frequency of data while using symbols or images that are relevant to the data. Example: 1. Ten students in class made a survey about their favourite sport. Here are the results. football tennis basketball football football tennis tennis football
Represent the given data in the form of frequency distribution and find the number of schools that are able to plant 50% of the plants or more? 95, 67, 28, 32, 65, 65, 69, 33, 98, 96, 76, 42 ... Frequency Distribution Worksheet. Explore math program. Math worksheets and visual curriculum. Get Started. FOLLOW CUEMATH. Facebook. Youtube ...
how often 2 occurs (5 times), etc, and wrote them down as a Frequency Distribution table. From the table we can see interesting things such as. getting 2 goals happens most often. only once did they get 5 goals. This is the definition: Frequency Distribution: values and their frequency (how often each value occurs). Here is another example:
DESCRIPTIVE STATISTICS WORKSHEET MTH 3210 SPRING 2016 5 (5) The following relative frequency distribution bar graph was created using Minitab (saved as a .jpg using \Copy Graph") A.2. Solution to Practice Problem 3.0.2. (1) The frequency distribution is summarized by the following table: Clutch Size Frequency 6 1 7 2 8 1 9 3 10 7 11 3 12 1 13 1
Statistics Creating Frequency Table & Histogram Showing Distribution of given data Math Worksheet Problems: This product involve Worksheets of Statistics related to histogram with answer key. Worksheets are made in 8.5" x 11" Standard Letter Size. This resource is helpful in students' assessment, group activities, practice and homework.
Math Worksheets. Videos that will help GMAT students review how to obtain the mean, median and mode from a frequency distribution table. Mean from a data frequency distribution. Illustration of the calculation of a frequency distribution mean Frequency Tables and Mean. Learn to find mean from data in a frequency table.
Construct the histogram that corresponds to frequency distribution constructed in part (c) for this data. For each integer that occurs in the data set, find the number of times it occurs divided by the number of values in the data set. So for example, 186 appears 3 times, and thus has relative frequency of 3 / 30 = 0.10 3 / 30 = 0.10.
1.1.8: Continuous Distribution (Worksheet) ... The student will construct relative frequency tables. The student will interpret results and their differences from different data groupings. 1.1.10: Descriptive Statistics (Worksheet) The student will construct a histogram and a box plot. The student will calculate univariate statistics.
Introduction to Statistics and Frequency Distributions. 3. should complete all of the practice problems. Most students benefit from a few repetitions . of each problem type. The additional practice helps consolidate what you have learned so you don't forget it during tests. Finally, use the activities and the practice problems to study. Then ...
Frequency is a way of tally how often the same data point appears in a data set. A frequency table is a visual that displays relative frequencies of the data points. To construct a frequency table we just list all of the data that appears in the set in ascending order vertically. We then mark a tally for every time the data appears in the set.
This quiz and worksheet can be used to help enhance the following skills: Problem solving - use acquired knowledge to solve frequency distribution table practice problems. Information recall ...
A frequency distribution table consists of at least two columns - one listing categories on the scale of measurement (X) and another for frequency (f). In the X column, values are listed from the highest to lowest, without skipping any. For the frequency column, tallies are determined for each value (how often each X value occurs in the data set).
We use frequency tables to find descriptive statistics. These are values which help describe the set of data such as the mean, median and mode of a set of data. For example, A frequency table showing the ages of 25 25 students on a college course. The mode is 18 18. The median is the 13^ {th} 13th value which is 18 18.
The following dataset holds the values for the measured heights of a group of patients in a doctor's chamber. To create a frequency distribution table and plot a histogram, follow the steps below. Steps: Select the range B6:C16 => Go to Insert tab => Select PivotTable inside Tables group.
Frequency Distributions. Fill out the rest of this simple distribution table by calculating the relative frequency, cumulative frequency, and cumulative percent. ... 100%. 9. 0.00. 55. 92%. 8. 10.17. 55. 92%. 7. 20.33. 45. 75%. 6. 25.42. 25. 42%. N = 60. Using the data set given below. Create a simple distribution table by calculating the ...
Try it risk-free for 30 days. Instructions: Choose an answer and hit 'next'. You will receive your score and answers at the end. question 1 of 3. You gathered data at a clinic and entered your ...
Worksheet #3: Categorical Frequency Distributions & Graphs 23 . Worksheet #4: Grouped Frequency Distributions & Graphs 24 . Lecture #4: Measures of Central Tendency 25 ... Worksheet #10: Intervals of Data 49 . Worksheet #11: Standard Scores 50 . Exam #1 - Descriptive Statistics - Sample 51 . Exam #1 - Descriptive Statistics - Sample ...
WORKSHEET - Extra examples (Chapter 1: sections 1.1,1.2,1.3) 1. Identify the population and the sample: ... Determine whether the numerical value is a parameter or a statistics (and explain): a) A recent survey by the alumni of a major university indicated that the average ... Construct a frequency distribution, frequency histogram, relative ...
Describing Data: Frequency Distributions and Graphic Presentation Chapter 2 GOALS When you have completed this chapter, you will be able to: • Organize raw data into a frequency distribution • Produce a histogram, a frequency polygon, and a cumulative frequency polygonfrom quantitative data • Develop and interpret a stem-and-leaf display • Present qualitative data using such graphical ...