The 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.
Explanation
(a)
Marks
Class boundary
Freq
Cum freq
0 - 9
0 - 9.5
4
4
10 - 19
9.5 - 19.5
5
9
20 - 29
19.5 - 29.5
6
15
30 - 39
29.5 - 39.5
12
27
40 - 49
39.5 - 49.5
8
35
50 - 59
49.5 - 59.5
5
40
(b) Mode = 35.5 (c) Median = where = lower class boundary of median class = 29.5 ; = cumulative frequency before median class = 15. = frequency of median class = 12, c = class interval = 10. Median = = =
