what is the standard deviation

Question

Calculate the standard deviation of the heights of the starting five on the​ women's basketball team if the heights are 180​ cm, 183​ cm, 177​ cm, 182​ cm, and 183 cm.

Answer 1

mean height = the arithmetic average = sum of the 5 heights divided by 5 = 181

mean differences for each=

1,2,4,1,2

mean differences squared

= 1, 4, 16, 1, 4

sum of squared differences =26

26/5 =5.2= variance

sqr5.2= about 2.3 = the population standard deviation

that treats the 5 starters as the total population

if it's treated as a sample, of a larger population of women basketball players, then divide by n-1 =5-1= 4, instead of 5

sqr(26/4) = about 2.55 = sample standard deviation