If the median and mode of 4 observations are 4, 6 respectively and the sum of squares of observations is 48, then the standard deviation is:

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Solution

The correct option is C
$G i v e n t h a t, m e d i a n = 4 a n d m o d e = 6. W e k n o w t h a t, M e a n - M o d e = 3 (M e a n - M e d i a n) M e a n - 6 = 3 (M e a n - 4) ¯ x - 6 = 3 ¯ x - 12 ¯ x = 3 σ^{2} = \frac{\sum x_{i}^{2}}{n} - {(\frac{\sum x^{i}}{n})}^{2} = \frac{48}{4} - (3)^{2} = 3 ∴ σ = \sqrt{3}$

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If the median and mode of 4 observations are 4, 6 respectively and the sum of squares of observations is 48, then the standard deviation is:

The correct option is C Given that, median=4 and mode=6.We know that,Mean−Mode=3 (Mean−Median)Mean−6=3(Mean−4)¯x−6=3¯x−12¯x=3σ2=∑x2in−(∑xin)2=484−(3)2=3∴ σ=√3