Two histograms, A and B, have been drawn for the same set of masses (in kg) of 120 students distributed into the following unequal class intervals:
Class intervals: 30–40, 40–55, 55–60, 60–70
For Histogram A the heights of the rectangles have been taken directly proportional to the class frequencies 12, 30, 38 and 40 respectively.
For Histogram B the heights of the rectangles have been taken proportional to the frequency densities 1.2, 2.0, 7.6 and 4.0 respectively.
Answer the following questions.
(i) State the formula for finding the frequency density of a class interval.
(ii) Verify the frequency density value for the class 55–60 kg.
(iii) Give two reasons why Histogram B gives a more faithful visual impression of the data than Histogram A.
(iv) If a reader looks only at Histogram A, which class interval are they most likely to consider the modal class? Give a reason based on the given frequencies.