For the following distribution, calculate mean using all suitable methods: Size of item: 1−4, 4−9, 9−16, 16−27. Frequency: 6, 12, 26, 20.

For the following distribution, calculate mean using all suitable

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 = $(\frac{\sum f_x}{\sum f})$

Therefore, Mean = $\frac{848}{64}$ = 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 + $(\frac{\sum f d}{\sum f})$

Therefore, Mean = 6.5 + $\frac{432}{64}$ = 6.5 + 6.75 = 13.25

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