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.

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.