how to get the standard deviation

Question

find the standard deviation of 14, 7,23,56,16,12,18,38,14,60,33,25,11,5,69,7,7,3,10,7,3,10,15,31

Answer 1

Given numbers 14,7,23,56,16,12,18,38,14,60,33,25,11,5,69,7,7,3,10,7,3,10,15,31

Mean of above numbers = (14+7+23+56+16+12+18+38+14+60+33+25+11+5+69+7+7+3+10+7+15+31)/24

= 494/24

= 20.58

To calculate the given numbers standard deviation, first compute the difference of each data point from the mean,and square the result of each.

(14-20.58)^2 = (-6.58)^2 = 43.29

(7-20.58)^2 = (-13.58)^2 = 184.41

(23-20.58)^2 = (2.42)^2 = 5.85

(56-20.58)^2 = (35.42)^2 = 1254.57

(16-20.58)^2 = (-4.58)^2 = 20.97

(12-20.58)^2 = (-8.58)^2 = 73.61

(18-20.58)^2 = (-2.58)^2 = 6.65

(38-20.58)^2 = (17.42)^2 = 303.45

(14-20.58)^2 = (-6.58)^2 = 43.29

(60-20.58)^2 = (39.42)^2 = 1553.93

(33-20.58)^2 = (12.42)^2 = 154.25

(25-20.58)^2 = (4.42)^2 = 19.53

(11-20.58)^2 = (-9.58)^2 = 91.77

(5-20.58)^2 = (-15.58)^2 = 242.73

(69-20.58)^2 = (48.42)^2 = 2344.49

(7-20.58)^2 = (-13.58)^2 = 184.41

(7-20.58)^2 = (-13.58)^2 = 184.41

(3-20.58)^2 = (-17.58)^2 = 309.05

(10-20.58)^2 = (-10.58)^2 = 111.93

(7-20.58)^2 = (-13.58)^2 = 184.41

(3-20.58)^2 = (-17.58)^2 = 309.05

(10-20.58)^2 = (-10.58)^2 = 111.93

(15-20.58)^2 = (-5.58)^2 = 31.13

(31-20.58)^2 = (10.42)^2 = 108.57

Next compute the mean of above values and square root it.

Mean = (43.29+184.41+5.85+1254.57+20.97+73.61+6.65+303.45+43.29+1553.93+154.25+19.53+91.77+242.73+

2344.49+184.41+184.41+309.05+111.93+184.41+309.05+111.93+31.13+108.57)/24

= 7877.42/24

= 328.23

Sqrt (328.23) = 18.11

Given numbers standard deviation is 18.11.