JEE Main 2016 · 10 Apr · Shift 1 · Mathematics Q86

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MathematicsSingle correct+4 / -1Question 86 of 90

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

2.4

2.8

2.5

2.6

Answer and worked solution

Official answer: B

As printed (variance 124), the two missing observations would be $8\pm\sqrt{288}$ and the mean deviation about 8.4, which is not an option. The data fit with variance 12.4: then $x+y=16$ , $x^2+y^2=146$ , so the observations are 5 and 11, and the mean deviation is $\frac{4+3+1+0+6}5=2.8$ . The derived key reads the variance as 12.4.

Topics:Variance and standard deviation Measures of central tendency

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JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 86