A survey regarding the heights (in cm) of 50 girls of class X of a

Q) A survey regarding the heights (in cm) of 50 girls of class X of a school was conducted and the following data was obtained :

Find the mean and mode of the above data.

Ans: 1. Mean value of the data:

Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency:

We know that, mean of grouped data is given by:

Mean of grouped data = $(\frac{\sum f_x}{\sum f})$

Therefore, Mean value = $\frac{7490}{50}$ = 149.8

Hence, the mean value of the given data is 149.8.

2. Mode value of the data:

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

In the given question, class “150 – 160” has frequency of 20 which is the highest frequency among all other classes.

Hence, modal class is “150 – 160”.

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 = 150

$f_1$ = frequency of modal class = 20

$f_0$ = frequency of class proceeding to modal class = 12

$f_2$ = frequency of class succeeding to modal class = 8

h = class size = 150 – 160 = 10

Let’s put values in the formula and solve:

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

= 150 + $[\frac{(20 - 12)}{(2 \times 20 - 12 - 8)}]$ x 10

= 150 + $(\frac{8}{20})$ x 10

= 150 + $\frac{8}{2}$ = 150 + 4 = 154

Hence, the mode value of given data is 154.

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