The average temperatures recorded in Bangalore for 8 days (in degrees celsius) are 23, 23.5, 27, 25.5, 24, 24.5, 21.5, 23. Find the variance of the temperatures.

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1.25

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2.5

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Solution

The correct option is D 2.5
$M e a n t e m p e r a t u r e (i n^{\circ} C) = \frac{1}{8} \times [23 + 23.5 + 27 + 25.5 + 24 + 24.5 + 21.5 + 23] = \frac{192}{8} = 24^{\circ} C$

$V a r i a n c e, σ^{2} = \frac{\sum (X - ¯ X)^{2}}{N} = \frac{1}{8} \times [1 + 0.25 + 9 + 2.25 + 0 + 0.25 + 6.25 + 1] \frac{20}{8} = 2.5$

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The average temperatures recorded in Bangalore for 8 days (in degrees celsius) are 23, 23.5, 27, 25.5, 24, 24.5, 21.5, 23. Find the variance of the temperatures.

The correct option is D 2.5Mean temperature (in ∘C)=18×[23+23.5+27+25.5 +24+24.5+21.5+23]=1928=24∘C Variance,σ2=∑(X−¯X)2N=18×[1+0.25+9+2.25+0+0.25+6.25+1]208=2.5