Q. 3 4.4( 8 Votes )

Heights of students of Class X are given in the following frequency distribution:

Find the modal height.

Also, find the mean height. Compare and interpret the two measures of central tendency.

Answer :

Here, the maximum class frequency is 20.

The class corresponding to this frequency is the modal class. modal class = 160 - 165

lower limit of the modal class (l) = 160

Modal class size (h) = 5

Frequency of the modal class (f1) = 20

Frequency of class preceding the modal class (f0) = 8

Frequency of class succeeding the modal (f2) = 12

Mode is given by,

Mode = 160 + 3 = 163

Hence, the mode is 163 cm.

Mode represents frequency, hence 163 cm is the height of maximum number of students.

To find the mean, we will solve by using direct method.

We have got

Σfi = 60 & Σfixi = 9670

mean is given by

Thus, mean is 161.17

Mean represents average, thus 161.7 cm is the average height of all the students.

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