Engineering
Mathematics
Measure of Central Tendency
Question

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is

6 : 7

5 : 8

4 : 9

10 : 3

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Solution

μ=1+3+8+x+y5

25 = 12 + x + y ⇒ x + y = 13 ……………….(1)

σ2=Σ(xi−μ)2N

9.2=1+9+64+x2+y25−25

34.2 × 5 = 74 + x2 + y2

171 = 74 + x2 + 2xy

97 = x2 + y2                   …………….(2)

(x + y)2 = x2 + y2 + 2xy

169 – 97 = 2xy ⇒ xy = 36

T = 4, 9

So ration is 49  or  94