Frequency distribution (II)







              In this page we are going to see grouped frequency distribution. If the data are with large number of events then it is difficult to arrange them. In order to table the values we have to divide them into class intervals.

Frequency distribution table

Example:

        Draw the frequency table for following data: The ages of 15 participants who had participated in a tournament.

         15,23,21,30,17,22,33,16,27,24,31,15,22,26,29.


While dividing the given data into class interval we have to keep it in mind that the class intervals must be mutually exclusive with equal width.

Solution:

Let us start dividing the given data into class intervals. For that we have to follow the steps given below:

  1. First we have to arrange in order.

     15, 15, 16, 17, 21, 22,22, 23, 24,26, 27, 29, 30,31,33

       2. We have to find the lowest and highest values to calculate the range.

Lowest value = 15

Highest value = 33

                                  Range = 33-15  =  18

        3.  Now we have to divide the range by the number of groups so that we will get the class interval.

                  Here we want 5 groups. So let us divide the range 18 by 6.

                                     18/5 = 3.6

                   The class interval here is 4.

Note: If we get decimal then we have to round that up to the nearest whole number.

      4. To form the classes we have to start from less than or equal to the smallest value.

            Starting at 14, the groups will be like this: 

                      Starting at 14, with the group size 4, we have the lower value of the class intervals as 14, 18, 22, 26, 30.

        5. Now let us table the frequencies. 

  •              The first four values of rearranged data are 15,15,16 and 17. So the frequency is 4 for the first interval. 
  •               The second class interval is 18-21. There is only one value in that interval. So the frequency is 1.
  •              The third class interval is 22-25. There are 4 values in that interval, which are  22, 22, 23 and 24. The frequency is 4.
  •               The fourth class interval is 26-29. There are 3 values in that interval, which are 26,27 and 29. The frequency is 3.
  •              The fifth class interval is 30-33. There are 3 values in that interval, which are 30,31 and 33. So the frequency is 3.

    Now let us first mark the data as tally mark and after that we enter the frequency.

  The frequency table has been  drawn for the given data. Let us practice some problems to draw frequency distribution table. Students follow the above method for making table. Parents and teachers can encourage the students to do the problems on their own. If they are having any doubt they can verify the steps with the solutions.  If you are having any doubt in the solutions, you can contact us through mail, we will help you to clear your doubt.

Practice problems:

  1. Construct a frequency table for the marks obtained by 25 students in a test conducted in the class:                                              37,76,56,77,89,24,63,82,54,26,77,56,76,63,52,28,44,65,72,98,43,34,87,91,79.
  2. The number of magazines sold in a shop for 10 days as follows:              24,30,32,27,36,21,33,30,37,25.                                                                                      
  3. The measurement of height of 15 students in a group in centimeters:                                                                                      134,129,130,137,140,133,128,132,131,132,128,137,129,125,136.                                                                      







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