The frequency distribution is given below:beg | vedclass

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(D) First,we calculate the mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(2 	imes 4) + (3 	imes 9) + (4 	imes 16) + (5 	imes 14) + (6 	im

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(D) First,we calculate the mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(2 \times 4) + (3 \times 9) + (4 \times 16) + (5 \times 14) + (6 \times 11) + (7 \times 6)}{4 + 9 + 16 + 14 + 11 + 6} = \frac{8 + 27 + 64 + 70 + 66 + 42}{60} = \frac{277}{60} \approx 4.6167$.
Using the formula for standard deviation $\sigma = \sqrt{\frac{\sum f_i x_i^2}{N} - \bar{x}^2}$:
$\sum f_i x_i^2 = (4 \times 4) + (9 \times 9) + (16 \times 16) + (14 \times 25) + (11 \times 36) + (6 \times 49) = 16 + 81 + 256 + 350 + 396 + 294 = 1393$.
$\sigma = \sqrt{\frac{1393}{60} - (4.6167)^2} = \sqrt{23.2167 - 21.3139} = \sqrt{1.9028} \approx 1.38$.

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$k^2-1$	$k^2-1$	$k^2-1$	$k-3$

Class Interval	$0$-$4$	$4$-$8$	$8$-$12$	$12$-$16$	$16$-$20$
Frequency	$2$	$4$	$6$	$3$	$1$

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

Similar Questions

If $1$ is added to each of the first $10$ natural numbers,then the variance of the numbers so obtained is:

If the variance of $6, 7, 8, 9, 10, 11$ is $\sigma^2$,then the variance of $12, 14, 16, 18, 20, 22$ is

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution:
$X_i$ $0$ $1$ $2$ $3$ $4$ $5$
$f_i$ $k+2$ $2k$ $k^2-1$ $k^2-1$ $k^2-1$ $k-3$
where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to:

The variance of the following frequency distribution is:
Class Interval $0$-$4$ $4$-$8$ $8$-$12$ $12$-$16$ $16$-$20$
Frequency $2$ $4$ $6$ $3$ $1$

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

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