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what is the standard deviation of the data set rounding to the nearest tenth?
56, 78, 124, 34, 67, 91, 20

Respuesta :

Edufirst
Formula: standard deviation, s:

s = √ (s^2)
       
s^2 = ∑ (xi - x)^2 / (n - 1)

where

xi are the individual data
x is the median of the data
n is the number of data.

Then, first find the number of data: n = 7

Next, find the media: x = [56 + 78 + 124 + 34 + 67 + 91 + 20] / 7 = 470 / 7 = 67.1

Next, find ∑ (xi - x)^2

(56 - 67.1)^2 + (78 - 67.1)^2 + (124 - 67.1)^2 + (34 - 67.1)^2 + (67 - 67.1)^2 +  (91 - 67.1)^2 + (20 - 67.1)^2

= 7,364.87

Finally: s^2 = [7364.87 / (7 - 1) ] = 1227.48 => s = √(1227.48) = 35.04

Answer: s = 35.04


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