**Q) **For the following distribution, calculate mean using all suitable methods:

**Ans: **

**1. Direct Method**

To calculate Mean value of the distribution, 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 = = 13.25

**Hence, the mean value of the given distribution data by Direct Method is 13.25**

**2. Assumed Mean Method:**

Let’s calculate midpoints and consider 6.5 as assumed mean, ∴ a = 6.5

Next, let’s rearrange the data in the following order:

By assumed mean method, mean of the grouped data is given by:

Mean of grouped data, X = a +

Therefore, Mean = 6.5 + = 6.5 + 6.75 = 13.25

**Hence, the mean value of the given distribution data by Assumed Mean method is 13.25**