JAMB Mathematics 2010 Paper

Concept:Standard deviation measures how far the data values spread from the arithmetic mean.It is obtained by taking the square root of the average of the squared deviations from the mean.Explanation:First, calculate the mean of the data set.$$\overline{x} = \frac{2 + 3 + 5 + 6}{4} = \frac{16}{4} = 4$$Next, find the deviation of each value from the mean and then square it.For $x = 2$: deviation $= 2 - 4 = -2$, squared $= (-2)^2 = 4$For $x = 3$: deviation $= 3 - 4 = -1$, squared $= (-1)^2 = 1$For $x = 5$: deviation $= 5 - 4 = 1$, squared $= 1^2 = 1$For $x = 6$: deviation $= 6 - 4 = 2$, squared $= 2^2 = 4$Sum the squared deviations.$$\sum (x - \overline{x})^2 = 4 + 1 + 1 + 4 = 10$$Now apply the standard deviation formula for a sample or population of $N = 4$.$$S = \sqrt{\frac{\sum (x - \overline{x})^2}{N}} = \sqrt{\frac{10}{4}} = \sqrt{\frac{5}{2}}$$Answer:Standard deviation $= \sqrt{\frac{5}{2}}$, so the correct option is D.