Respuesta :
Answer:
The sample mean of 75.6 inches is the same as the population mean but the sample standard deviation of 6.2 inches differs from the population standard deviation of 5.5 inches.
Step-by-step explanation:
We are given the heights, in inches, of the starting five players on a college basketball team : 69, 72, 78, 74, and 85.
Heights (X) [tex]X-\bar X[/tex] [tex]( X - \bar X)^{2}[/tex]
69 -6.6 43.56
72 -3.6 12.96
78 2.4 5.76
74 -1.6 2.56
85 9.4 88.36
Total 153.2
Firstly, as we know that the formula for calculating Population mean and sample mean is same which is given as;
Population Mean = Sample Mean = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{69+72+78+74+85}{5}[/tex] = 75.6 inches.
Now, formula for calculating population and sample standard deviation is given as;
Population standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n} }[/tex]
= [tex]\sqrt{\frac{153.2}{5} }[/tex] = 5.5 inches
And, Sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{153.2}{4} }[/tex] = 6.2 inches
Therefore, the sample mean of 75.6 inches is the same as the population mean but the sample standard deviation of 6.2 inches differs from the population standard deviation of 5.5 inches.
