The mean of the following distribution is: x i 10 13 16 19 f i 2 5 7 6 Options: A . &nbsp15.2 B . &nbsp15.35 C . &nbsp15.55 D . &nbsp16

The mean of the following distribution is: xi10131619fi2576

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 sumof 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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