To find the five-number summary of the basketball players' heights (66, 70, 63, 75, 66), we first need to organize the numbers from smallest to largest: 63, 66, 66, 70, 75. The five-number summary includes the smallest number (63), the first quartile (66), the median (66), the third quartile (70), and the largest number (75). So, the five-number summary is: 63, 66, 66, 70, 75.
Next, to find the standard deviation, we use these steps: First, find the average (mean) height: (63 + 66 + 66 + 70 + 75) / 5 = 68. Then, we calculate the difference of each height from the mean, square those differences, and find the average of the squared differences. The differences are -5 (63-68), -2 (66-68), -2 (66-68), 2 (70-68), and 7 (75-68). Squaring those gives us 25, 4, 4, 4, and 49. Then we add those up (25 + 4 + 4 + 4 + 49 = 86) and divide by the number of players (5): 86 / 5 = 17.2. Finally, we take the square root of 17.2, which is about 4.14. So, the standard deviation is about 4.14 inches.