JAMB Mathematics 2014 Paper

Concept:Standard deviation measures how spread out the numbers are from the arithmetic mean.It is the square root of the average of the squared deviations from the mean.Explanation:First, find the mean of the given data set.The data values are $5, 4, 3, 2, 1$.Mean $\bar{x} = \frac{5 + 4 + 3 + 2 + 1}{5} = \frac{15}{5} = 3$.Subtract the mean from each value to obtain the deviation $d = x - \bar{x}$.Square each deviation to obtain $d^2$.The calculations are shown in the table below.The total of the squared deviations is $\sum d^2 = 4 + 1 + 0 + 1 + 4 = 10$.The number of observations is $n = 5$.Standard deviation $\sigma = \sqrt{\frac{\sum d^2}{n}}$.Substitute the obtained values into the formula.$\sigma = \sqrt{\frac{10}{5}} = \sqrt{2}$.Answer:The standard deviation of $5, 4, 3, 2, 1$ is $\sqrt{2}$.This corresponds to option A.