29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106;...

29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

What is the Standard deviation (please round to two decimal places)?

Expert Solution

Solution:

Given that,

29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

The mean of sample is

x/n = (29+37+38+ 40+5+67+68+69+ 76+86+ 87+95+96+ 96+ 99+106+ 112+ 127+ 145+150) / 20

= 81.4

The sample mean is 81.4

Sample standard deviation is s

s = $\sqrt$ 1/(n-1)(x - )²

⁼ $\sqrt$ 1/4 (29 - 81.4 )²+ (37-81.4)²+ (38 - 81.4)²+ (40- 81.4 )² +( 58- 81.4)²+ (67 -81.4)²+ (68 - 81.4 )²+ (69- 81.4)² +( 76 - 81.4 )²+ (86 - 81.4 )²+ (87 - 81.4 )²+ (95- 81.4 )² +( 96 - 81.4)²+ (96 -81.4 )²+ (99 - 81.4 )²+ (106- 81.4 )² +( 112 - 81.4 )²+ (127 - 81.4)²+ (145 -81.4)²+ (150- 81.4 )²

= $\sqrt$ 1477.2

= 38.434359627812

The sample standard deviation is =38.43

orchestra answered 1 year ago

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