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WAEC Further Mathematics 2014 Paper

Question : 34

Total: 40

Find the variance of 1, 2, 0, -3, 5, -2, 4.

Solution:

Concept:

Variance measures the average squared deviation of each data value from the mean.

Explanation:

First, find the mean of the data set.

\overline{x} = \frac{1 + 2 + 0 + (-3) + 5 + (-2) + 4}{7} = \frac{7}{7} = 1

Next, compute each squared deviation

(x - \overline{x})^{2}

For

x = 1

(1-1)^2 = 0

; for

x = 2

(2-1)^2 = 1

For

x = 0

(0-1)^2 = 1

; for

x = -3

(-3-1)^2 = 16

For

x = 5

(5-1)^2 = 16

; for

x = -2

(-2-1)^2 = 9

For

x = 4

(4-1)^2 = 9

Sum of squared deviations:

0 + 1 + 1 + 16 + 16 + 9 + 9 = 52

Number of observations,

n = 7

Variance

= \frac{\sum (x - \overline{x})^{2}}{n} = \frac{52}{7}

Answer:

\frac{52}{7}

(Option A)

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