**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 =

Therefore, Mean value = = 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 + x h

Here,

L = lower class limit of modal class = 150

_{ }= frequency of modal class = 20

_{ }= frequency of class proceeding to modal class = 12

_{ }= 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 + x h

= 150 + x 10

= 150 + x 10

= 150 + = 150 + 4 =** 154**

**Hence, the mode value of given data is 154.**

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