The mean and standard deviation of 20 observa | vedclass

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(D) Given: $n = 20$,$\bar{x} = 10$,$\sigma = 2.5$. Incorrect sum of observations: $\Sigma x_i = n 	imes \bar{x} = 20 	imes 10 = 200$. Correct sum of

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$(10.5, 26)$

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(D) Given: $n = 20$,$\bar{x} = 10$,$\sigma = 2.5$. Incorrect sum of observations: $\Sigma x_i = n 	imes \bar{x} = 20 	imes 10 = 200$. Correct sum of observations: $\Sigma x_i = 200 - 25 + 35 = 210$. Correct mean $\alpha = \frac{210}{20} = 10.5$. Incorrect sum of squares: $\sigma^2 = \frac{\Sigma x_i^2}{n} - (\bar{x})^2 \implies (2.5)^2 = \frac{\Sigma x_i^2}{20} - 10^2$. $6.25 = \frac{\Sigma x_i^2}{20} - 100 \implies \Sigma x_i^2 = 20 	imes 106.25 = 2125$. Correct sum of squares: $\Sigma x_i^2 = 2125 - 25^2 + 35^2 = 2125 - 625 + 1225 = 2725$. Correct variance $\beta = \frac{\Sigma x_i^2}{n} - (\alpha)^2 = \frac{2725}{20} - (10.5)^2 = 136.25 - 110.25 = 26$. Thus,$(\alpha, \beta) = (10.5, 26)$.

Class	Frequency
$0 - 20$	$17$
$20 - 40$	$f_1$
$40 - 60$	$32$
$60 - 80$	$f_2$
$80 - 100$	$19$
Total	$120$

$Country$	$Agriculture$	$Industries$	$Services$	$Others$
$India$	$45$	$19$	$28$	$4$
$U.K.$	$3$	$40$	$44$	$13$
$Japan$	$6$	$48$	$43$	$3$
$U.S.A.$	$3$	$35$	$61$	$1$

Similar Questions

The mean and variance of a data of $10$ observations are $10$ and $2$, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become $10.1$ and $1.99$, respectively. Then $\alpha + \beta$ equals.

If the arithmetic mean of the following frequency distribution is $50$,find the values of $f_1$ and $f_2$.
Class Frequency
$0 - 20$ $17$
$20 - 40$ $f_1$
$40 - 60$ $32$
$60 - 80$ $f_2$
$80 - 100$ $19$
Total $120$

If the coefficients of variation of two distributions are $40$ and $20$ and their variances are $144$ and $64$ respectively,then the mean of their arithmetic means is
$(A)$ $40$
$(B)$ $12$
$(C)$ $30$
$(D)$ $35$

The following data was collected from a newspaper: (percentage distribution). It is an example of
$Country$ $Agriculture$ $Industries$ $Services$ $Others$
$India$ $45$ $19$ $28$ $4$
$U.K.$ $3$ $40$ $44$ $13$
$Japan$ $6$ $48$ $43$ $3$
$U.S.A.$ $3$ $35$ $61$ $1$

The mean and variance of seven observations are $8$ and $16$,respectively. If $5$ of the observations are $2, 4, 10, 12, 14$,then the product of the remaining two observations is

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