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Maths > Data Handling > Frequency Distribution and Data: Types, Tables, and Graphs
Data Handling

Frequency Distribution and Data: Types, Tables, and Graphs

Frequency distribution in statistics provides the information of the number of occurrences (frequency) of distinct values distributed within a given period of time or interval, in a list, table, or graphical representation. Grouped and Ungrouped are two types of Frequency Distribution. Data is a collection of numbers or values and it must be organized for it to be useful. Let us take a look at data and its frequency distribution.

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Data

Any bit of information that is expressed in a value or numerical number is data. For example, the marks you scored in your Math exam is data, and the number of cars that pass through a bridge in a day is also data. Data is basically a collection of information, measurements or observations.

Raw data is an initial collection of information. This information has not yet been organized. After the very first step of data collection, you will get raw data. For example, we go around and ask a group of five friends their favourite colour. The answers are Blue, Green, Blue, Red, and Red. This collection of information is the raw data.

Then there is discrete data and continuous data. Discrete data is that which is recorded in whole numbers, like the number of children in a school or number of tigers in a zoo. It cannot be in decimals or fractions. Continuous data need not be in whole numbers, it can be in decimals. Examples are the temperature in a city for a week, your percentage of marks for the last exam etc.

Browse more Topics under Data Handling

Frequency

The frequency of any value is the number of times that value appears in a data set. So from the above examples of colours, we can say two children like the colour blue, so its frequency is two. So to make meaning of the raw data, we must organize. And finding out the frequency of the data values is how this organisation is done.

Frequency Distribution

Many times it is not easy or feasible to find the frequency of data from a very large dataset. So to make sense of the data we make a frequency table and graphs. Let us take the example of the heights of ten students in cms.

Frequency Distribution Table

139, 145, 150, 145, 136, 150, 152, 144, 138, 138

Frequency distribution table

This frequency table will help us make better sense of the data given. Also when the data set is too big (say if we were dealing with 100 students) we use tally marks for counting. It makes the task more organised and easy. Below is an example of how we use tally marks.

Frequency distribution

 

Frequency Distribution Graph

Using the same above example we can make the following graph:

Frequency-distribution-graph

Learn more about Bar Graphs and Histogram here.

Types of Frequency Distribution

  • Grouped frequency distribution.
  • Ungrouped frequency distribution.
  • Cumulative frequency distribution.
  • Relative frequency distribution.
  • Relative cumulative frequency distribution.

Grouped Data

At certain times to ensure that we are making correct and relevant observations from the data set, we may need to group the data into class intervals. This ensures that the frequency distribution best represents the data. Let us make a grouped frequency data table of the same example above of the height of students.

Class Interval Frequency
130-140 4
140-150 3
150-160 3

From the above table, you can see that the value of 150 is put in the class interval of 150-160 and not 140-150. This is the convention we must follow.

Solved Example for You

Question 1: The table gives the number of snacks ordered and the number of days as a tally. Find the frequency of snacks ordered.

Answer: From the frequency table the number of snacks ordered ranging between

  • 2-4  is 4 days
  • 4 to 6  is 3 days
  • 6 to 8 is 9 days
  • 8 to 10 is 9 days
  • 10 to 12 is 7 days.

So the frequencies for all snacks ordered are 4, 3, 9, 9, 7

Frequency Distribution and Data: Types, Tables, and Graphs

Question 2: How to find frequency distribution?

Answer: We can find frequency distribution by the following steps:

  • First of all, calculate the range of the data set.
  • Next, divide the range by the number of the group you want your data in and then round up.
  • After that, use class width to create groups
  • Finally, find the frequency for each group.

Question 3: Define frequency distribution in statistics?

Answer: In an overview, the frequency distribution of all distinct values in some variables and the number of times they occur. Meaning that it tells how frequencies are distributed overvalues in a frequency distribution. However, mostly we use frequency distributions to summarize categorical variables.

Question 4: Why are frequency distributions important?

Answer: It has great importance in statistics. Also, a well-structured frequency distribution makes possible a detailed analysis of the structure of the population with respect to given characteristics. Therefore, the groups into which the population break down can be determined.

Question 5: State the components of frequency distribution?

Answer: The various components of the frequency distribution are: Class interval, types of class interval, class boundaries, midpoint or class mark, width or size o class interval, class frequency, frequency density = class frequency/ class width, relative frequency = class frequency/ total frequency, etc.

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