Question

Question 4 15 pts Following are heights, in inches, for a sample of college basketball players. 84 88 78 85 70 75 72 86 78 81 86 78 81 72 73 76 77 87 88 60 a. Find the mean, median and mode. (3pts) b. Use the mean, median and mode to describe the shape of the distribution. (4pts) c. Find the standard deviation and variance of the heights of the basketball players. (4pts) d. Find the percentile for 85in, that is find k such that Pa = 85.4pts) Upload Choose a File

Answer 1

- R RGui (64-bit) File Edit Packages Windows Help O RR Console x 1 > x = c(84,88, 78,85, 70, 75, 72,86,78,81,86,78,81, 72, 73, 76, 77,87,88,60) > length(x) [1] 20 > table (x) х 60 70 72 73 75 76 77 78 81 84 85 86 87 88 1 1 2 1 1 1 3 2 1 1 2 1 2 > mean (x) R Untitled - R Editor [1] 78.75 x = c(84,88,78,85, 70, 75, 72,86,78,81,86,78,81,72,73,76, 77,87,88 > median (x) length (x) [1] 78 > sd (x) table (x) [1] 7.253856 mean (x) >ecdf (x) (85) median (x) [1] 0.75 > 1 sd (x) ecdf (x) (85)

I've used R 4.0.1 to compute the values.

a. mean = 78.75, median = 78, mode = 78 (as the value 78 has highest frequency i.e. 3)

b. As mean > median, mode, it can be said that the distribution is positively skewed. But more or less symmetric as the difference is very small.

c. The standard deviation is = 7.253856

d. k = 0.75, that is to say, it is 3rd quartile.