Theory question 103
Data PresentationThe table below shows the marks obtained by forty pupils in a mathematics test
Marks: 0 – 9, 10 – 19, 20 – 29, 30 – 39, 40 – 49, 50 – 59
No. of Pupils: 4, 5, 6, 12, 8, 5
(a) Draw a histogram for the mark distribution. (b) Use your histogram to estimate the mode (c) Calculate the median of the distribution.
Show the model answer
(a) Class boundaries −0.5 (or 0), 9.5, 19.5, 29.5, 39.5, 49.5, 59.5 on the marks axis; bars of heights 4, 5, 6, 12, 8, 5 with no gaps; suitable scale and labelled axes.
(b) Modal class is 30 – 39 (the tallest bar). Join the top corners of the tallest bar to the adjacent corners of the neighbouring bars; the crossing point gives mode ≈ 29.5 + (12 − 6)/((12 − 6) + (12 − 8)) × 10 = 35.5 (accept about 35 to 36).
(c) Median position = 40/2 = 20th pupil. Cumulative frequencies: 4, 9, 15, 27, 35, 40, so the median class is 30 – 39.
Median = 29.5 + (20 − 15)/12 × 10 = 29.5 + 4.17 = 33.67 (≈ 33.7).
For a grouped median use L + ((N/2 − cumulative frequency before the class)/class frequency) × class width.