Mean of 5 observations is 7. If four of these | vedclass

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Question

Let ${5^{th}}$ observation be $x$.

Given mean $=7$

$	herefore 7 = \frac{{6 + 7 + 8 + 10 + x}}{5}$

$ \Rightarrow x = 4$ Now, Variance&nb

Vedclass · Accepted Answer

$2$

Vedclass · Answer

Let ${5^{th}}$ observation be $x$.

Given mean $=7$

$	herefore 7 = \frac{{6 + 7 + 8 + 10 + x}}{5}$

$ \Rightarrow x = 4$ Now, Variance 

$ = \sqrt {\frac{{{{\left( {6 - 7} ight)}^2} + {{\left( {7 - 7} ight)}^2} + {{\left( {8 - 7} ight)}^2} + {{\left( {10 - 7} ight)}^2} + {{\left( {4 - 7} ight)}^2}}}{5}} $

$ = \sqrt {\frac{{{1^2} + {0^2} + {1^2} + {3^2} + {3^2}}}{5}}  = \sqrt {\frac{{20}}{5}}  = \sqrt 4  = 2$

$X_i$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_i$	$3$	$6$	$16$	$\alpha$	$9$	$5$	$6$

${x_i}$	$3$	$8$	$13$	$18$	$25$
${f_i}$	$7$	$10$	$15$	$10$	$6$

Mean of $5$ observations is $7.$ If four of these observations are $6, 7, 8, 10$ and one is missing then the variance of all the five observations is

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