The table below shows the distribution of scores obtained by a group of candidates in an examination: | Score (x) | 2 | 4 | 6 | 8 | 10 | |---|---|---|---|---|---| | Frequency (f) | 1 | 2 | 6 | 2 | 1 | Calculate the variance of the scores.

The table below shows the distribution of scores obtained by a group of candidates in an e… — JAMB UTME

The table below shows the distribution of scores obtained by a group of candidates in an examination:

Score ( $x$ )	2	4	6	8	10
Frequency ( $f$ )	1	2	6	2	1

Calculate the variance of the scores.

Cevap: 4

The variance of the scores is 4.

The mean score is

\bar{x} = 6

. Summing the weighted squared deviations gives

\sum f(x - 6)^2 = 48

. Dividing by the total frequency

N = 12

results in a variance of

\frac{48}{12} = 4

Find the total frequency and calculate the mean score.

Total frequency

N = 12

and mean

\bar{x} = 6

The mean is given by

\bar{x} = \frac{\sum f x}{\sum f} = \frac{2 + 8 + 36 + 16 + 10}{12} = \frac{72}{12} = 6

Determine the sum of squared deviations multiplied by their frequencies.

\sum f(x - \bar{x})^2 = 48.

Evaluating each term:

1(2-6)^2 = 16

2(4-6)^2 = 8

6(6-6)^2 = 0

2(8-6)^2 = 8

, and

1(10-6)^2 = 16

. Summing these yields

16 + 8 + 0 + 8 + 16 = 48

Compute the variance by dividing the total squared deviations by the total frequency.

Variance = 4.

Variance is

\sigma^2 = \frac{\sum f(x - \bar{x})^2}{\sum f} = \frac{48}{12} = 4

Variance of a Frequency Distribution