Cumulative Frequency Diagrams and Histograms — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Frequency density = frequency ÷ class width.
8÷10 = 0.8; 20÷10 = 2.0
Question 2
(a)In a histogram, it is the area of each bar (not its height) that represents the frequency. Using frequency density as the height ensures the area correctly reflects frequency even when class widths differ.
Using frequency density keeps bar area, not height, proportional to frequency — essential when class widths are unequal
Question 3
(a)Frequency density = frequency ÷ class width.
18 ÷ 6 = 3
Question 4
(a)The y-axis of a cumulative frequency diagram shows the running total (cumulative frequency) of all values up to that point.
Cumulative (running total) frequency
Question 5
(a)Find half of the total frequency (40th value position) on the y-axis, then read across to the curve and down to the x-axis.
Read across from cumulative frequency = 40 (half of 80) to the curve, then down to the x-axis
Question 6
(a)Frequency = frequency density × class width.
4 × 5 = 20
Question 7
(a)Frequency = frequency density × class width.
4 × 5 = 20
Question 8
(a)Median is at the (n/2)th value; upper quartile is at the (3n/4)th value.
Median at the 40th value; upper quartile at the 60th value
Question 9
(a)IQR = upper quartile − lower quartile.
60 − 25 = 35
Question 10
(a)Continuous data has no natural gaps between categories, so bars are drawn touching, with area (not height) representing frequency to correctly handle unequal class widths.
Continuous data has no gaps between values, so bars are drawn touching, and area (not just height) must represent frequency
Book a free trial class
Tell us a little about your requirement.