First slide

Introduction to statistics

Question

If the arithmetic mean of the following distribution is 8.2, then $a =$
$\begin{array}{cccccccc} x_{i} & : & 1 & 3 & 5 & 9 & 11 & 13 \\ f_{i} & : & 3 & 2 & 7 & a & 4 & 8 \end{array}$

Moderate

A

5
B

6
C

9
D

none of these

Solution

We have
$\begin{array}{l} \frac{1 \times 3 + 3 \times 2 + 5 \times 7 + 9 a + 11 \times 4 + 13 \times 8}{3 + 2 + 7 + a + 4 + 8} = 8.2 \\ \Rightarrow \frac{3 + 6 + 35 + 9 a + 44 + 104}{24 + a} = 8.2 \\ \Rightarrow 9 a + 192 = 24 \times 8.2 + 8.2 a \Rightarrow 0.8 a = 4.8 \Rightarrow a = 6 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App