First slide

Introduction to statistics

Question

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1 ,2 and 6, then the other two are

Moderate

A

2 and 9
B

3 and 8
C

4 and 7
D

5 and 6

Solution

Let the two unknown items be x and y, then
$Mean = 4 \Rightarrow \frac{1 + 2 + 6 + x + y}{5} = 4$
$\Rightarrow x + y = 11 - - - - (1)$
and variance = 5.2
$\Rightarrow \frac{1^{2} + 2^{2} + 6^{2} + x^{2} + y^{2}}{5} - (mean)^{2} = 5.2$
$41 + x^{2} + y^{2} = 5 [5.2 + (4)^{2}]$
$41 + x^{2} + y^{2} = 106$
$x^{2} + y^{2} = 65 - - - - - (2)$
$Solving (1) and (2) for x and y, we get$
$x = 4, y = 7 or x = 7, y = 4$

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