Question

Find the sample standard deviation and the population standard deviation of the data set. 56, 65, 73, 66, 64, 58, 72, 52, 69, 71, 53, 66, 78, 58

Answer 1

Answer:

population standard deviation = √58.79857 =  7.6680

sample standard deviation = √63.32154 = 7.9575

Step-by-step explanation:

The question is on sample standard deviation and population standard deviation

Arrange data in ascending order

56, 65, 73, 66, 64, 58, 72, 52, 69, 71, 53, 66, 78, 58

52,53,56,58,58,64,65,66,66,69,71,72,73,78

Find the mean of the data set;

$(52+53+56+58+58+64+65+66+66+69+71+72+73+78) /14$

=$\frac{901}{14} = 64.36$

Finding the deviations from the mean

              Deviations           square of deviations

52-64.36= -12.36                  152.77

53-64.36= -11.36                   129.05

56-64.36= -8.36                     69.89

58-64.36= -6.36                     40.45

58-64.36= -6.36                      40.45

64-64.36= -0.36                         0.13

65-64.36= 0.64                          0.41

66-64.36= 1.64                           2.67

66-64.36=  1.64                          2.67

69-64.36= 4.64                         21.53

71-64.36=6.64                           44.09

72-64.36=7.64                           58.37

73-64.36=8.64                            74.65

78-64.36=13.64                          186.05

Sum                                             823.18        

1. Treating the data set as an entire population;

population variance= 823.18/14 =58.79857

population standard deviation = √58.79857 =  7.6680

2. Treating the data set as a sample, the number of data points will be less by 1

n= 14-1 = 13

sample variance= 823.18/13 = 63.32154

sample standard deviation = √63.32154 = 7.9575