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;
[tex](52+53+56+58+58+64+65+66+66+69+71+72+73+78) /14[/tex]
=[tex]\frac{901}{14} = 64.36[/tex]
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
