Heights of students of Class X are given in the following frequency distribution: [CBSE 2014]

Height (in cm)	150 - 155	155 - 160	160 - 165	165 - 170	170 - 175
Number of students	15	8	20	12	5

Find the modal height.

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

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

Σf_i = 60 & Σf_ix_i = 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.