Question

The scores of 5 students in an examination are: 6, 5, 8, 7 and 4. Find the variance.
a. 3
b. 2
c. 2.5
d. 4.5

Answer 1

The scores of 5 students in an examination are: 6, 5, 8, 7 and 4. Find the variance.

a. 3 b. 2 c. 2.5 d. 4.5

Solution

The formula for measuring an unbiased estimate of the population variance from a fixed sample of $n$ observations is the following:

$$s ^ {2} = \frac {\sum_ {i} ^ {n} (x _ {i} - \bar {x}) ^ {2}}{n - 1}$$

where

$s^2 =$ Variance

$\Sigma =$ Summation, which means the sum of every term in the equation after the summation sign.

$x_{i} =$ Sample observation. This represents every term in the set.

$\bar{x} =$ The mean. This represents the average of all the numbers in the set.

$n =$ The sample size. You can think of this as the number of terms in the set.

In our case

$$\bar {x} = \frac {6 + 5 + 8 + 7 + 4}{5} = 6$$

and

$$s ^ {2} = \frac {(6 - 6) ^ {2} + (5 - 6) ^ {2} + (8 - 6) ^ {2} + (7 - 6) ^ {2} + (4 - 6) ^ {2}}{5 - 1} = \frac {0 ^ {2} + 1 ^ {2} + 2 ^ {2} + 1 ^ {2} + 2 ^ {2}}{4} = \frac {0 + 1 + 4 + 1 + 4}{4} = 2.5$$

Answer: c. 2.5.