The standard deviation of the numbers 22 ,   26 ,   28 ,   20 ,   24 ,   30 is

Question

The standard deviation of the numbers 22 , &#160; 26 , &#160; 28 , &#160; 20 , &#160; 24 , &#160; 30 is

Aicharya · Accepted Answer

We know that S . D = &#8721; x i - &#956; 2 N where, &#956; &#8594; Mean N &#8594; Number of terms x i &#8594; terms Now, &#956; = 22 + 26 + 28 + 20 + 24 + 30 6 &#8658; &#956; = 150 6 = 25 Now, x i x i - &#956; 2 22 22 - 25 2 = 9 26 26 - 25 2 = 1 28 28 - 25 2 = 9 20 20 - 25 2 = 25 24 24 - 25 2 = 1 30 30 - 25 2 = 25 Therefore, &#8721; x i - &#956; 2 = 70 S . D = 70 6 = 3 . 42

$x_{i}$	${(x_{i} - μ)}^{2}$
$22$	${(22 - 25)}^{2} = 9$
$26$	${(26 - 25)}^{2} = 1$
$28$	${(28 - 25)}^{2} = 9$
$20$	${(20 - 25)}^{2} = 25$
$24$	${(24 - 25)}^{2} = 1$
$30$	${(30 - 25)}^{2} = 25$

The standard deviation of the numbers 22 , &#160; 26 , &#160; 28 , &#160; 20 , &#160; 24 , &#160; 30 is

Solution

The standard deviation of the numbers 22 , 26 , 28 , 20 , 24 , 30 is