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

$Let the two unknown numbers be x and y, then mean = 4 = \frac{1 + 2 + 6 + x + y}{5} = 4$
$\Rightarrow x + y = 11 \dots \dots \dots \dots \dots \dots \dots (1)$
$σ^{2} = 5.2$
$\frac{1^{2} + 2^{2} + 6^{2} + x^{2} + y^{2}}{5} - {(m e a n)}^{2} = 5.2$
$41 + x^{2} + y^{2} = 5 [5.2 + 4^{2}]$
$x^{2} + y^{2} = 65 \dots \dots \dots \dots \dots . . . (2)$
Solve (1) & (2)
$x = 4, y = 7$

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