### Question 12

The table shows the distribution of the heights of a group of people.

 Height (m) 0.4 – 0.5 0.6 – 0.9 1.0 – 1.2 1.3 – 1.4 1.5 – 1.7 Number of people 2 8 12 6 6
1. Draw a histogram to illustrate the distribution.
2. Using an assumed mean of 1.1 m, find, correct to one decimal place, the mean height of the group.

### Observation

The Chief Examiner reported that majority of the candidates attempted this question. The report further stated that majority of them performed poorly in part (a). They reportedly showed poor knowledge of histograms with unequal class intervals. In part (a), candidates were expected to calculate the frequency density for each class interval and use it to draw the required histogram.

 Height (m) f Class Boundaries Class Size (c) Frequency density (f/c) Class Mark d fd 0.4 – 0.5 2 0.35 – 0.55 0.2 10 0.45 -0.65 -1.3 0.6 – 0.9 8 0.55 – 0.95 0.4 20 0.75 -0.35 -2.8 1.0 – 1.2 12 0.95 – 1.25 0.3 40 1.10 0 0 1.3 – 1.4 6 1.25 – 1.45 0.2 30 1.35 0.25 1.5 1.5 – 1.7 6 1.45 – 1.75 0.3 20 1.60 0.50 3 Σf = 34 Σfd = 0.4

The histogram would then be drawn with the frequency density on the vertical axis and the class boundary on the horizontal axis.
The mean was calculated using the formula, mean = A + , where A = assumed mean and d = deviations from the assumed mean. Therefore, mean = 1.1 +  = 1.1, correct to one decimal place.