The test scores of five students in a mathematics quiz are 5, 8, 11, 12, and 14. What is t… — JAMB UTME

The test scores of five students in a mathematics quiz are $5, 8, 11, 12,$ and $14$ . What is the variance of these test scores?

The variance of the test scores is

10

The mean of the scores is

10

. Subtracting

10

from each score gives deviations of

-5, -2, 1, 2,

and

4

. Squaring these gives

25, 4, 1, 4,

and

16

, which sum to

50

. Dividing this sum by the number of data points (

5

) yields a variance of

10

Calculate the mean (

\bar{x}

) of the data set

\bar{x} = \frac{5 + 8 + 11 + 12 + 14}{5} = \frac{50}{5} = 10

The mean is required to find the deviation of each score from the central value.

Compute the squared deviations from the mean

(x_i - \bar{x})^2

(5-10)^2 = 25

(8-10)^2 = 4

(11-10)^2 = 1

(12-10)^2 = 4

(14-10)^2 = 16

Squaring deviations ensures all negative differences become positive.

Find the sum of all squared deviations

\sum (x_i - \bar{x})^2 = 25 + 4 + 1 + 4 + 16 = 50

Summing the squared deviations measures total variation around the mean.

Divide the total sum of squared deviations by the number of data values (

N = 5

)

\text{Variance } (\sigma^2) = \frac{50}{5} = 10

Variance is defined as the average of the squared deviations.

Variance of Ungrouped Data

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