The following table gives the heights (in cm) of a group of 55 students in a class : 140-142 ,142- 144, 144-146, 146 - 148, 148- 150, 150 - 152, 152 - 154 154-156 No of students 4,6,9,12,9,7,3,5. find the modal height of the students.

The following table gives the heights (in cm) of a group of 55

Q) The following table gives the heights (in cm) of a group of 55 students in a class.

Compute the modal height and interpret the result.

Ans: Since the modal class is the class with the highest frequency.

In the given question, class “146 – 148” has 12 students (i.e. highest frequency of 12).

Hence, modal class is “146-148”.

Now mode of the grouped data is calculated by:

Mode = L + $[\frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)}]$ x h

Here,

L = lower class limit of modal class = 146

$f_1$ = frequency of modal class = 12

$f_0$ = frequency of class proceeding to modal class = 9

$f_2$ = frequency of class succeeding to modal class = 9

h = class size = 148 – 146 = 2

Let’s put values in the formula and solve:

Mode = L + $[\frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)}]$ x h

= 146 + $[\frac{(12 - 9)}{(2 \times 12 - 9 - 9)}]$ x 2

= 146 + $(\frac{3}{6})$ x 2

= 146 + 1

= 147

Hence, the modal height of the class is 147 cm

Interpretation of the result:

The height of maximum students in the class is 147 cm.

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