The height (in inches) of the starting 5 players on the intramural basketball team is shown.

66, 70, 63, 75, 66

What is the five number summary of the data?

What is the standard deviation of the data?

Show your work.

don't explain in calculations but full sentences, explain in one sentence

1 answer

To find the five-number summary, we first arrange the heights in ascending order: 63, 66, 66, 70, 75. The five-number summary consists of the minimum (63), first quartile (Q1, which is 66), median (Q2, which is 66), third quartile (Q3, which is 70), and maximum (75). Therefore, the five-number summary is 63, 66, 66, 70, 75.

Next, to calculate the standard deviation, we first find the mean of the data, which is 66. The deviations from the mean are calculated, squared, and then averaged. The squared deviations are (63-66)² = 9, (66-66)² = 0, (66-66)² = 0, (70-66)² = 16, and (75-66)² = 81. The variance is the average of these squared deviations, which is (9 + 0 + 0 + 16 + 81)/5 = 21. The standard deviation is then the square root of the variance, resulting in approximately 4.58.

In summary, the five-number summary of the players' heights is 63, 66, 66, 70, 75, and the standard deviation of the data is approximately 4.58 inches.