A collections of human skulls is divided into three classes A, B and C according to the value of a length-breadth index X. Skulls with X<65 are classified as A (long headed), those with 6570 as C (short headed). The percentages in the three classes in this collection are 58, 38 and 4. Find approximate the mean and standard deviation of X, on the assumption that X is normally distributed.
The sum is 33 and there are 5 data points. Therefore, the mean is 33 ÷ 5 = 6.6. Then we each
value in data set, subtract the mean and square the difference. For instance, for the first value:
(2 - 6.6) 2 = 21.16
The squared differences for all values are added:
21.16 + 0.16 + 12.96 + 29.16 + 5.76 = 69.20
The sum is then divided by the number of data points:
69.20 ÷5 = 13.84
The variance is 13.84. To get the standard deviation, you calculate the square root of the
variance, which is 3.72.