QJEEM19Madaf4: JEE Main 2019 Mathematics - Class 11 JEEM19Madaf4 Solution: If the standard deviation of the numbers –1, 0, 1, k is 5 where …

Question

Verified Solution • 2025–26 Session moderate

If the standard deviation of the numbers –1, 0, 1, k is

\sqrt{5}

where k > 0, then k is equal to

Accepted Answer

standard deviation =

\sqrt{5}

∴

Variance =

{(\sqrt{5})}^{2}

= 5

Also variance =

\frac{\sum x_{i}^{2}}{N} - μ^{2}

Where

μ

= Mean =

\frac{- 1 + 0 + 1 + k}{4}

=

\frac{k}{4}

∴

Variance =

\frac{{(- 1)}^{2} + 0 + 1^{2} + k^{2}}{4}

-

\frac{k^{2}}{16}

\Rightarrow

5 =

\frac{2 + k^{2}}{4}

-

\frac{k^{2}}{16}

\Rightarrow

8 + 3k² = 80

\Rightarrow

k² = 24 = 2

\sqrt{6}

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