Question

A child, (and mathematical genius!) wishes to estimate the variability in the number of candies he can collect from houses during trick-or-treating.

He randomly selects a sample of 20 houses, and records the number of candies he gets at each:

# Candies # Houses
0 3
1 7
2 3
3 4
4 3

Find the sample variance he calculates using this data.

Answer 1

Variance is calculated as the square of the standard deviation. Hence, we have to calculate the standard deviation first. Its formula is

s = sqrt{[∑(x - X)^2 ]÷ (n-1)]}

where x is the value of each single data, X is the mean, and n is the number of samples. The mean would be

X = (0 + 1 + 2 + 3 + 4)/5 = 2

Then,

∑(x - X)^2 = (0-2)^2 + (1-2)^2 + (2-2)^2 + (3-2)^2 + (4-2)^2 = 10

Thus,

s = sqrt{10÷ (20-1)]} = 0.725

The square of this would be the variance.

Variance = (0.725)^2 = 0.526

Therefore, the sample variance of the data is 0.526.