Question

find the range and the standard deviation of the data set 8.4, 7.7, 8.6, 7.5, 8.9, 7.8, 8.6, 9.1, 8.0

Answer 1

arranging the data in ascending order , we get

7.5 , 7.7 , 7.8 , 8.0 , 8.4 , 8.6 , 8.6 , 8.9 , 9.1

range is given by the difference of highest and smallest number

so range = 9.1 - 7.5

range = 1.6

7.5 , 7.7 , 7.8 , 8.0 , 8.4 , 8.6 , 8.6 , 8.9 , 9.1

mean of the data set is given as ::

mean = (7.5 + 7.7 + 7.8 + 8.0 + 8.4 + 8.6 + 8.6 + 8.9 + 9.1)/4

mean = 18.65

7.5 , 7.7 , 7.8 , 8.0 , 8.4 , 8.6 , 8.6 , 8.9 , 9.1

new data is determined by subtracting each value in above data set from mean

18.65 - 7.5 = 11.15

18.65 - 7.7 = 10.95

18.65 - 7.8 = 10.85

18.65 - 8.0 = 10.65

18.65 - 8.4 = 10.25

18.65 - 8.6 = 10.05

18.65 - 8.6 = 10.06

18.65 - 8.9 = 9.75

18.65 - 9.1 = 9.55

taking square of each values and adding them together , we get

variance = (11.15² + 10.95² + 10.85² + 10.65² + 10.25² + 10.05² + 10.06² + 9.75² + 9.55² )/4

variance = 242.226

standard deviation = sqrt (variance) = sqrt (242.226)

standard deviation = 15.56