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.
| 1. | What is Frequency Distribution? |
| 2. | Frequency Distribution Graphs |
| 3. | Types of Frequency Distribution |
| 4. | Frequency Distribution Tables |
| 5. | FAQs on Frequency Distribution |
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.
| Quiz Marks | No. of Students |
|---|---|
| 15 | 2 |
| 17 | 3 |
| 20 | 3 |
| 14 | 2 |
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.
| Marks obtained in Test (class intervals) | No. of Students (Frequency) |
|---|---|
| 0 – 5 | 3 |
| 6 – 10 | 4 |
| 11 – 15 | 5 |
| 16 – 20 | 8 |
| Total | 20 |
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).
| Marks obtained in Test | No. of Students |
|---|---|
| 5 | 3 |
| 10 | 4 |
| 15 | 5 |
| 18 | 4 |
| 20 | 4 |
| Total | 20 |
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.
Frequency Distribution Examples
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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.
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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, 36Solution: 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.
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