Question

5. Calculate the standard deviation by using the formula for the following sample of vehicle speeds on the 202: 68, 72, 83, 63, 65, 76, 70Fill in the table:

Answer 1

we have the data set

68, 72, 83, 63, 65, 76, 70

step 1

Find out the mean

mean=(68+72+83+63+65+76+70)/7

mean=497/7

mean=71

step 2

Find out the deviation from the mean

68---------> 71-68=3

72 -------> 72-71=1

83 -------> 83-71=12

63 -----> 71-63=8

65 -----> 71-65=6

76 -----> 76-71=5

70 ----> 71-70=1

step 3

Find out the deviation^2

68 -----------> 3^2=9

72 --------> 1^2=1

83---------> 12^2=144

63 -----> 8^2=64

65 ----> 6^2=36

76 ----> 5^2=25

70 ---> 1^2=1

step 4

Sum all values of step 3

Sum=(9+1+144+64+36+25+1)

Sum=280

Divide by the number of points

280/7=40

To find out the standard deviation take the square root

SD=6.325