Theory question 106
StatisticsThe table shows the marks obtained by groups of students in a class test.
Marks: 40−44, 45−49, 50−54, 55−59, 60−64, 65−69
No. of Students: 4, 9, 18, 23, 10, 6
(a) Draw a histogram for the distribution.
(b) Use your histogram to estimate the median of the distribution.
Show the model answer
Model answer
(a) Class boundaries 39.5, 44.5, 49.5, 54.5, 59.5, 64.5, 69.5 on the x-axis; bars of heights 4, 9, 18, 23, 10, 6, all of width 5
(b) N = 70, so the median is the 35th mark; cumulative frequencies 4, 13, 31, 54 put it in the 54.5 − 59.5 bar
Median ≈ 54.5 + (35 − 31)/23 × 5 ≈ 55.4 (an estimate of about 55 to 56 from the histogram)
Explanation
Use class boundaries so the bars touch; the median splits the total area in half.