Year 8 Charts & Quartiles Questions
1. [Q12, November 2012 2H] The frequency table gives information about the times it took some office workers to get to the office one day.
Time (t minutes) / Frequency0 t £10 / 4
10 t £ 20 / 8
20 t £ 30 / 14
30 t £ 40 / 16
40 t £ 50 / 6
50 t £ 60 / 2
(a) Draw a frequency polygon for this information.
(2)
(b) Write down the modal class interval.
......
(1)
One of the office workers is chosen at random.
(c) Work out the probability that this office worker took more than 40 minutes to get to the office.
......
(2)
(Total for Question 12 is 5 marks)
2. [Q6 Nov 2009 3H] 30 students took a test.
The table shows information about how long it took them to complete the test.
Time (t minutes) / Frequency0 < t £ 10 / 5
10 < t £ 20 / 7
20 < t £ 30 / 8
30 < t £ 40 / 6
40 < t £ 50 / 4
(a) On the grid, draw a frequency polygon for this information.
(2)
(b) Write down the modal class interval.
...... (1)
Cumulative Frequency and Box Plots
3. The table shows information about the heights of 40 bushes.
Height (h cm) / Frequency170 £ h < 175 / 5
175 £ h < 180 / 18
180 £ h < 185 / 12
185 £ h < 190 / 4
190 £ h < 195 / 1
(a) Complete the cumulative frequency table.
Height(h cm) / CumulativeFrequency
170 £ h < 175
170 £ h < 180
170 £ h < 185
170 £ h < 190
170 £ h < 195
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(c) Use the graph to find an estimate for the median height of the bushes.
……………………… cm
4. 40 boys each completed a puzzle.
The cumulative frequency graph below gives information about the times it took them to complete the puzzle.
(a) Use the graph to find an estimate for the median time
...... seconds
(1)
For the boys
the minimum time to complete the puzzle was 9 seconds
and the maximum time to complete the puzzle was 57 seconds.
(b) Use this information and the cumulative frequency graph to draw a box plot showing information about the boy’s times.
(3)
The box plot below shows information about the times taken by 40 girls to complete the same puzzle.
(c) Make two comparisons between the boys’ times and the girls’ times.
......
......
(2)
5. The table gives information about the ages of 160 employees of an IT company.
Age (A) in years / Frequency15 < A £ 25 / 44
25 < A £ 35 / 56
35 < A £ 45 / 34
45 < A £ 55 / 19
55 < A £ 65 / 7
(a) Write down the modal class interval.
......
(b) Complete the cumulative frequency table.
Age (A) in years / Cumulative Frequency15 < A £ 25
15 < A £ 35
15 < A £ 45
15 < A £ 55
15 < A £ 65
(1)
(c) On the grid below, draw a cumulative frequency graph for your table.
(d) Use your graph to find an estimate for
(i) the median age of the employees, ...... years
(i) the interquartile range of the ages of the employees...... years
Another IT company has 80 employees. The age of the youngest employee is 24 years.
The age of the oldest employee is 54 years. The median age is 38 years. The lower quartile age is 30 years. The upper quartile age is 44 years.
(e) On the grid below, draw a box plot to show information about the ages of the employees.
Diagram for part (e).
6. A company tested 100 batteries. The table shows information about the number of hours that the batteries lasted.
Time (t hours) / Frequency50 ≤ t < 55 / 12
55 ≤ t < 60 / 21
60 ≤ t < 65 / 36
65 ≤ t < 70 / 23
70 ≤ t < 75 / 8
(a) Complete the cumulative frequency table for this information.
(1)
Time(t hours) / Cumulative frequency
50 ≤ t < 55 / 12
50 ≤ t < 60
50 ≤ t < 65
50 ≤ t < 70
50 ≤ t < 75
(b) On the grid, draw a cumulative frequency graph for your completed table.
(c) Use your completed graph to find an estimate for the median time.
You must state the units of your answer.
......
(2)
7. Here are four cumulative frequency diagrams.
Here are four box plots.
For each box plot, write down the letter of the appropriate cumulative
frequency diagram.
P and ......
Q and ......
R and ......
S and ......
(Total 2 marks)
8. Here is the cumulative frequency curve of the weights of 120 girls at Mayfield
Secondary School.
Use the cumulative frequency curve to find an estimate for the
(i) median weight,
...... kg
(ii) interquartile range of the weights.
...... kg
(Total 3 marks)