The mean of the following distribution is: xi10131619fi2576

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Question

The mean of the following distribution is:
$\begin{matrix} x_{i} & 10 & 13 & 16 & 19 f_{i} & 2 & 5 & 7 & 6 \end{matrix}$

Options:

A . 15.2

B . 15.35

C . 15.55

D . 16

Answer: Option C
:
C

We know that,
Average or mean value of a given number of observations is the sum of all the observations divided by the total number of observations.
$\Rightarrow Mean = \frac{\sum x_{i} f_{i}}{\sum f_{i}}$
Now,
$\sum x_{i}$ $f_{i} = 20 + 65 + 112 + 114 = 311$
$\sum f_{i} = 20$
So,
$Mean = \frac{\sum x_{i} f_{i}}{\sum f_{i}} = \frac{311}{20} = 15.55$

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