Draw cumulative frequency graph from frequency table (unequal class widths)

Questions providing a frequency table with clearly unequal class widths where students must calculate cumulative frequencies and draw the graph, requiring care with x-axis scaling.

10 questions · Easy -1.3

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CAIE S1 2021 March Q5
9 marks Easy -1.3
5 A driver records the distance travelled in each of 150 journeys. These distances, correct to the nearest km , are summarised in the following table.
Distance \(( \mathrm { km } )\)\(0 - 4\)\(5 - 10\)\(11 - 20\)\(21 - 30\)\(31 - 40\)\(41 - 60\)
Frequency12163266204
  1. Draw a cumulative frequency graph to illustrate the data. \includegraphics[max width=\textwidth, alt={}, center]{3f05dc2a-b466-40bc-9f5f-0fd2bff120c8-06_1593_1397_852_415}
  2. For 30\% of these journeys the distance travelled is \(d \mathrm {~km}\) or more. Use your graph to estimate the value of \(d\).
  3. Calculate an estimate of the mean distance travelled for the 150 journeys.
CAIE S1 2011 June Q5
8 marks Easy -1.3
5 A hotel has 90 rooms. The table summarises information about the number of rooms occupied each day for a period of 200 days.
Number of rooms occupied\(1 - 20\)\(21 - 40\)\(41 - 50\)\(51 - 60\)\(61 - 70\)\(71 - 90\)
Frequency103262502818
  1. Draw a cumulative frequency graph on graph paper to illustrate this information.
  2. Estimate the number of days when over 30 rooms were occupied.
  3. On \(75 \%\) of the days at most \(n\) rooms were occupied. Estimate the value of \(n\).
CAIE S1 2016 June Q7
11 marks Easy -1.3
7 The amounts spent by 160 shoppers at a supermarket are summarised in the following table.
Amount spent \(( \\) x )\(\)0 < x \leqslant 30\(\)30 < x \leqslant 50\(\)50 < x \leqslant 70\(\)70 < x \leqslant 90\(\)90 < x \leqslant 140$
Number of shoppers1640482630
  1. Draw a cumulative frequency graph of this distribution.
  2. Estimate the median and the interquartile range of the amount spent.
  3. Estimate the number of shoppers who spent more than \(\\) 115$.
  4. Calculate an estimate of the mean amount spent.
CAIE S1 2017 November Q2
5 marks Easy -1.8
2 The time taken by a car to accelerate from 0 to 30 metres per second was measured correct to the nearest second. The results from 48 cars are summarised in the following table.
Time (seconds)\(3 - 5\)\(6 - 8\)\(9 - 11\)\(12 - 16\)\(17 - 25\)
Frequency10151742
  1. On the grid, draw a cumulative frequency graph to represent this information. \includegraphics[max width=\textwidth, alt={}, center]{ee1e5987-315b-48eb-8dba-b9d4d34c87c9-03_1207_1406_897_411}
  2. 35 of these cars accelerated from 0 to 30 metres per second in a time more than \(t\) seconds. Estimate the value of \(t\).
OCR MEI S1 2005 June Q2
8 marks Easy -1.3
2 Answer part (i) of this question on the insert provided.
A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.
Length
\(( x\) miles \()\)
\(0 < x \leqslant 1\)\(1 < x \leqslant 2\)\(2 < x \leqslant 3\)\(3 < x \leqslant 4\)\(4 < x \leqslant 6\)\(6 < x \leqslant 10\)
Number of
journeys
3830211498
  1. On the insert, draw a cumulative frequency diagram to illustrate the data.
  2. Use your graph to estimate the median length of journey and the quartiles. Hence find the interquartile range.
  3. State the type of skewness of the distribution of the data.
OCR MEI S1 Q3
8 marks Easy -1.3
3 Answer part (i) of this question on the insert provided. A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.
Length
\(( x\) miles \()\)
\(0 < x \leqslant 1\)\(1 < x \leqslant 2\)\(2 < x \leqslant 3\)\(3 < x \leqslant 4\)\(4 < x \leqslant 6\)\(6 < x \leqslant 10\)
Number of
journeys
3830211498
  1. On the insert, draw a cumulative frequency diagram to illustrate the data.
  2. Use your graph to estimate the median length of journey and the quartiles. Hence find the interquartile range.
  3. State the type of skewness of the distribution of the data.
OCR MEI S1 Q4
9 marks Easy -1.8
4 Answer part (i) of this question on the insert provided. A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.
Length
\(( x\) miles \()\)
\(0 < x \leqslant 1\)\(1 < x \leqslant 2\)\(2 < x \leqslant 3\)\(3 < x \leqslant 4\)\(4 < x \leqslant 6\)\(6 < x \leqslant 10\)
Number of
journeys
3830211498
  1. On the insert, draw a cumulative frequency diagram to illustrate the data.
  2. Use your graph to estimate the median length of journey and the quartiles. Hence find the interquartile range.
  3. State the type of skewness of the distribution of the data.
CAIE S1 2023 March Q1
8 marks Moderate -0.8
Each year the total number of hours, \(x\), of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table.
\(x\)\(30 \leqslant x < 60\)\(60 \leqslant x < 90\)\(90 \leqslant x < 110\)\(110 \leqslant x < 140\)\(140 \leqslant x < 180\)\(180 \leqslant x \leqslant 240\)
Number of years48142572
  1. Draw a cumulative frequency graph to illustrate the data. [3]
  2. Use your graph to estimate the 70th percentile of the data. [2]
  3. Calculate an estimate for the mean number of hours of sunshine in Kintoo during June over the last 60 years. [3]
CAIE S1 2002 June Q2
6 marks Easy -1.2
The manager of a company noted the times spent in 80 meetings. The results were as follows.
Time (\(t\) minutes)\(0 < t \leq 15\)\(15 < t \leq 30\)\(30 < t \leq 60\)\(60 < t \leq 90\)\(90 < t \leq 120\)
Number of meetings4724387
Draw a cumulative frequency graph and use this to estimate the median time and the interquartile range. [6]
CAIE S1 2014 November Q6
9 marks Easy -1.2
On a certain day in spring, the heights of 200 daffodils are measured, correct to the nearest centimetre. The frequency distribution is given below.
Height (cm)\(4 - 10\)\(11 - 15\)\(16 - 20\)\(21 - 25\)\(26 - 30\)
Frequency2232784028
  1. Draw a cumulative frequency graph to illustrate the data. [4]
  2. 28\% of these daffodils are of height \(h\) cm or more. Estimate \(h\). [2]
  3. You are given that the estimate of the mean height of these daffodils, calculated from the table, is 18.39 cm. Calculate an estimate of the standard deviation of the heights of these daffodils. [3]