Mathematics, 21.05.2020 01:08 mtinoco

The heights, in inches, of the starting five players on a college basketball team are 69, 72, 78, 74, and 85. Considering the players as a sample, the mean and standard deviation of the heights are 75.6 inches and 6.2 inches, respectively. When the players are regarded as a population, the mean and standard deviation of the heights are 75.6 inches and 5.5 inches, respectively. Explain why, numerically, 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. QUIZLET

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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) $X-\bar X$ $( X - \bar X)^{2}$

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 = $\frac{\sum X}{n}$

= $\frac{69+72+78+74+85}{5}$ = 75.6 inches.

Now, formula for calculating population and sample standard deviation is given as;

Population standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n} }$

= $\sqrt{\frac{153.2}{5} }$ = 5.5 inches

And, Sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$

= $\sqrt{\frac{153.2}{4} }$ = 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.

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The heights, in inches, of the starting five players on a college basketball team are 69, 72, 78, 74...