Find the variance of the following discrete f | vedclass

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(D) Step $1$: Find the mid-points $(x_i)$ of each class interval: $x_1 = 1, x_2 = 3, x_3 = 5, x_4 = 7, x_5 = 9$. Step $2$: Calculate the mean $(\bar{x

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$\frac{88}{15}$

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(D) Step $1$: Find the mid-points $(x_i)$ of each class interval: $x_1 = 1, x_2 = 3, x_3 = 5, x_4 = 7, x_5 = 9$. Step $2$: Calculate the mean $(\bar{x})$: $\sum f_i = 2+3+5+3+2 = 15$. $\sum f_i x_i = (2 	imes 1) + (3 	imes 3) + (5 	imes 5) + (3 	imes 7) + (2 	imes 9) = 2 + 9 + 25 + 21 + 18 = 75$. $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{75}{15} = 5$. Step $3$: Calculate the variance $(\sigma^2)$: $\sigma^2 = \frac{\sum f_i (x_i - \bar{x})^2}{\sum f_i}$. $\sum f_i (x_i - 5)^2 = 2(1-5)^2 + 3(3-5)^2 + 5(5-5)^2 + 3(7-5)^2 + 2(9-5)^2$. $= 2(16) + 3(4) + 5(0) + 3(4) + 2(16) = 32 + 12 + 0 + 12 + 32 = 88$. $\sigma^2 = \frac{88}{15}$.

\text{Particulars}	\text{Firm } $A$ \text{ and Firm } $B$
\text{No. of wage earners}	$A: 586, B: 648$
\text{Mean of monthly wages}	$A: Rs. 5253, B: Rs. 5253$
\text{Variance of wages}	$A: 100, B: 121$

$X$	$35$	$54$	$52$	$53$	$56$	$58$	$52$	$50$	$51$	$49$
$Y$	$108$	$107$	$105$	$105$	$106$	$107$	$104$	$103$	$104$	$101$

Class Interval	Frequency
$0 - 6$	$10$
$6 - 12$	$8$
$12 - 18$	$6$
$18 - 24$	$4$
$24 - 30$	$2$

Find the variance of the following discrete frequency distribution:
Class Interval $0-2$ $2-4$ $4-6$ $6-8$ $8-10$
Frequency $(f_i)$ $2$ $3$ $5$ $3$ $2$

Similar Questions

Calculate the variance of the following continuous frequency distribution:
Class Interval $0$–$4$ $4$–$8$ $8$–$12$ $12$–$16$
Frequency $(f_i)$ $1$ $2$ $2$ $1$

The variance of the first $10$ natural numbers which are multiples of $3$ is

From the prices of shares $X$ and $Y$ below,find out which is more stable in value:

$X$ $35$ $54$ $52$ $53$ $56$ $58$ $52$ $50$ $51$ $49$

$Y$ $108$ $107$ $105$ $105$ $106$ $107$ $104$ $103$ $104$ $101$

The variance of the following frequency distribution is
Class Interval Frequency
$0 - 6$ $10$
$6 - 12$ $8$
$12 - 18$ $6$
$18 - 24$ $4$
$24 - 30$ $2$

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Find the variance of the following discrete frequency distribution: Class Interval$0-2$$2-4$$4-6$$6-8$$8-10$Frequency $(f_i)$$2$$3$$5$$3$$2$