This question was on statistics, requiring the calculation of mean and
standard deviation. It was well attempted by most candidates who were able to get the mean but failed to get the standard deviation. They were supposed to get the mid-values of the class interval (x), multiply each mid-value by its corresponding class interval frequency (fx), add these products (∑fx) and divide the result by the total frequency (∑f) i.e ∑fx . This gives the mean. ∑fx = 420, ∑f = 30.
∑f
Therefore mean (x) = 420 = 14.
30
To get the standard deviation, for each value of x, calculate its deviation from the mean (x) i.e (x – x), square it (i.e (x – x)²), and multiply by its corresponding class frequency i.e f(x – x)².
Add all these product values together (∑f(x – x)² and divide by the total frequency to get the variance i.e
∑f(x – x)² = 830 = 83
∑f 30 3
standard deviation = √ 83/3 = 5.26 to 2 decimal places.
