Frequency distribution: begin{array}{|l|l|l|l|l|l|l|} hline X & 2 & 3 & 4 & 5 &

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13.Statistics

medium

The frequency distribution:

$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$

Find the standard deviation.

Option A

Option B

Option C

Option D

Solution

$\begin{array}{|c|c|c|c|c|} \hline x_{i} & f_{i} & d_{i}=x_{i}-4 & f_{i} d_{i} & f_{i} d_{i}^{2} \\ \hline 2 & 4 & -2 & -8 & 16 \\ \hline 3 & 9 & -1 & -9 & 9 \\ \hline 4 & 16 & 0 & 0 & 0 \\ \hline 5 & 14 & 1 & 14 & 14 \\ \hline 6 & 11 & 2 & 22 & 44 \\ \hline 7 & 6 & 3 & 18 & 54 \\ \hline \text { Total } & n=60 & & \Sigma f_{i}=37 & \Sigma f_{i} d_{i}^{2}=137 \\ \hline \end{array}$

$ \therefore \quad SD =\sqrt{\frac{\Sigma f_{i} d_{i}^{2}}{n}-\left(\frac{\Sigma f_{i} d_{i}}{n}\right)^{2}}=\sqrt{\frac{137}{60}-\left(\frac{37}{60}\right)^{2}}=\sqrt{2.2833-(0.616)^{2}} $

$=\sqrt{2.2833-0.3794}=\sqrt{1.9037}=1.38 $

Standard 11

Mathematics

The mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$. If $M$ is the mean deviation of the numbers about the mean, then $25\; M$ is equal to

hard

(JEE MAIN-2022)

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normal

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hard

(JEE MAIN-2023)

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medium

(JEE MAIN-2021)

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easy

The frequency distribution: $\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$ Find the standard deviation.