Question

multiple choice 1 point
the average height for the players on a high school basketball team is 72 inches with a standard deviation of zero. interpret this information
there are no players that are 72 inches tall.
every player on the team is 72 inches tall.
half the team is taller than 72 inches and half the team is shorter than 72 inches.
fill in the blank 1 point
sample annual salaries (in thousands of dollars) for employees at a company are listed.
50 54 55 64 39 39 50 54 55 25 64 50 53
the sample standard deviation is s = type your answer. thousand dollars. round to 1 decimal place.

Explanation:

5.

The standard - deviation measures the amount of variation or dispersion of a set of values. A standard deviation of zero means there is no variation. So, if the average height of players on a high - school basketball team is 72 inches with a standard deviation of zero, every player's height is equal to the mean height, which is 72 inches.

Step1: Calculate the mean

The data set is \(x = \{50,54,55,64,39,39,50,54,55,25,64,50,53\}\).
The number of data points \(n = 13\).
The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{50 + 54+55+64+39+39+50+54+55+25+64+50+53}{13}=\frac{658}{13}\approx50.6\)

Step2: Calculate the squared differences

\((x_1-\bar{x})^2=(50 - 50.6)^2=0.36\), \((x_2 - 50.6)^2=(54 - 50.6)^2 = 11.56\), \((x_3-50.6)^2=(55 - 50.6)^2 = 19.36\), \((x_4-50.6)^2=(64 - 50.6)^2=179.56\), \((x_5-50.6)^2=(39 - 50.6)^2 = 134.56\), \((x_6-50.6)^2=(39 - 50.6)^2 = 134.56\), \((x_7-50.6)^2=(50 - 50.6)^2=0.36\), \((x_8-50.6)^2=(54 - 50.6)^2 = 11.56\), \((x_9-50.6)^2=(55 - 50.6)^2 = 19.36\), \((x_{10}-50.6)^2=(25 - 50.6)^2 = 655.36\), \((x_{11}-50.6)^2=(64 - 50.6)^2=179.56\), \((x_{12}-50.6)^2=(50 - 50.6)^2=0.36\), \((x_{13}-50.6)^2=(53 - 50.6)^2 = 5.76\)

Step3: Calculate the sum of squared differences

\(\sum_{i = 1}^{n}(x_{i}-\bar{x})^2=0.36+11.56+19.36+179.56+134.56+134.56+0.36+11.56+19.36+655.36+179.56+0.36+5.76 = 1352.4\)

Step4: Calculate the sample standard deviation

The formula for the sample standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^2}{n - 1}}\)
\(s=\sqrt{\frac{1352.4}{13 - 1}}=\sqrt{\frac{1352.4}{12}}=\sqrt{112.7}=10.6\)

Answer:

B. Every player on the team is 72 inches tall.

6.