The standard deviation of 7 observations 1, 2 | vedclass

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(B) The given observations are $1, 2, 3, 4, 5, 6, 7$.The mean $(\bar{x})$ is calculated as:$\bar{x} = \frac{1+2+3+4+5+6+7}{7} = \frac{28}{7} = 4$.The

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(B) The given observations are $1, 2, 3, 4, 5, 6, 7$.The mean $(\bar{x})$ is calculated as:$\bar{x} = \frac{1+2+3+4+5+6+7}{7} = \frac{28}{7} = 4$.The variance $(\sigma^2)$ is calculated using the formula $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$:$\sigma^2 = \frac{(1-4)^2 + (2-4)^2 + (3-4)^2 + (4-4)^2 + (5-4)^2 + (6-4)^2 + (7-4)^2}{7}$$\sigma^2 = \frac{(-3)^2 + (-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2}{7}$$\sigma^2 = \frac{9 + 4 + 1 + 0 + 1 + 4 + 9}{7} = \frac{28}{7} = 4$.The standard deviation $(\sigma)$ is the square root of the variance:$\sigma = \sqrt{4} = 2$.

Size $(x_i)$	$3.5$	$4.5$	$5.5$	$6.5$	$7.5$	$8.5$	$9.5$
Frequency $(f_i)$	$3$	$7$	$22$	$60$	$85$	$32$	$8$

The standard deviation of $7$ observations $1, 2, 3, 4, 5, 6, 7$ is:

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