Draw histogram then perform other calculations

Questions that ask students to draw a histogram from a frequency table with unequal class widths, then perform other statistical work such as finding specific frequencies, comparing distributions, or other calculations not covered by the above categories.

13 questions · Moderate -0.6

2.02b Histogram: area represents frequency
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CAIE S1 2023 June Q5
7 marks Moderate -0.3
5 The populations of 150 villages in the UK, to the nearest hundred, are summarised in the table.
Population\(100 - 800\)\(900 - 1200\)\(1300 - 2000\)\(2100 - 3200\)\(3300 - 4800\)
Number of villages812504832
  1. Draw a histogram to represent this information. \includegraphics[max width=\textwidth, alt={}, center]{a7157882-d87e-4efb-abc5-9c9f58197012-08_1395_1195_1043_516}
  2. Write down the class interval which contains the median for this information.
  3. Find the greatest possible value of the interquartile range for the populations of the 150 villages.
CAIE S1 2024 June Q3
6 marks Moderate -0.3
3 The heights, in cm, of 200 adults in Barimba are summarised in the following table.
Height \(( h \mathrm {~cm} )\)\(130 \leqslant h < 150\)\(150 \leqslant h < 160\)\(160 \leqslant h < 170\)\(170 \leqslant h < 175\)\(175 \leqslant h < 195\)
Frequency1632766412
  1. Draw a histogram to represent this information. \includegraphics[max width=\textwidth, alt={}, center]{a909cef1-8a22-4cef-b0b7-c48316304c0c-04_1397_1495_762_287}
  2. The interquartile range is \(R \mathrm {~cm}\). Show that \(R\) is not greater than 15 .
CAIE S1 2022 March Q3
6 marks Moderate -0.8
3 At a summer camp an arithmetic test is taken by 250 children. The times taken, to the nearest minute, to complete the test were recorded. The results are summarised in the table.
Time taken, in minutes\(1 - 30\)\(31 - 45\)\(46 - 65\)\(66 - 75\)\(76 - 100\)
Frequency2130688645
  1. Draw a histogram to represent this information. \includegraphics[max width=\textwidth, alt={}, center]{c1bc5ac2-6b0e-48c7-92e9-9b8b56b57d90-05_1000_1198_785_516}
  2. State which class interval contains the median.
  3. Given that an estimate of the mean time is 61.05 minutes, state what feature of the distribution accounts for the median and the mean being different.
CAIE S1 2024 March Q3
8 marks Moderate -0.8
3 The times taken, in minutes, by 150 students to complete a puzzle are summarised in the table.
Time taken
\(( t\) minutes \()\)
\(0 \leqslant t < 20\)\(20 \leqslant t < 30\)\(30 \leqslant t < 35\)\(35 \leqslant t < 40\)\(40 \leqslant t < 50\)\(50 \leqslant t < 70\)
Frequency82335522012
  1. Draw a histogram to represent this information. \includegraphics[max width=\textwidth, alt={}, center]{d1a3524c-a3b5-45fe-86a7-5cbda087efcd-06_1193_1489_886_328}
  2. Calculate an estimate for the mean time for these students to complete the puzzle.
  3. In which class interval does the lower quartile of the times lie?
CAIE S1 2020 November Q7
10 marks Moderate -0.3
7 A particular piece of music was played by 91 pianists and for each pianist, the number of incorrect notes was recorded. The results are summarised in the table.
Number of incorrect notes\(1 - 5\)\(6 - 10\)\(11 - 20\)\(21 - 40\)\(41 - 70\)
Frequency105263218
  1. Draw a histogram to represent this information. \includegraphics[max width=\textwidth, alt={}, center]{9f0f0e3c-7baf-42eb-a4fb-9ce61922c3cd-10_1488_1493_785_365}
  2. State which class interval contains the lower quartile and which class interval contains the upper quartile. Hence find the greatest possible value of the interquartile range.
  3. Calculate an estimate for the mean number of incorrect notes.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
CAIE S1 2014 June Q7
11 marks Moderate -0.8
7 A typing test is taken by 111 people. The numbers of typing errors they make in the test are summarised in the table below.
Number of typing errors\(1 - 5\)\(6 - 20\)\(21 - 35\)\(36 - 60\)\(61 - 80\)
Frequency249211542
  1. Draw a histogram on graph paper to represent this information.
  2. Calculate an estimate of the mean number of typing errors for these 111 people.
  3. State which class contains the lower quartile and which class contains the upper quartile. Hence find the least possible value of the interquartile range.
CAIE S1 2015 June Q2
5 marks Moderate -0.8
2 The table summarises the lengths in centimetres of 104 dragonflies.
Length \(( \mathrm { cm } )\)\(2.0 - 3.5\)\(3.5 - 4.5\)\(4.5 - 5.5\)\(5.5 - 7.0\)\(7.0 - 9.0\)
Frequency825283112
  1. State which class contains the upper quartile.
  2. Draw a histogram, on graph paper, to represent the data.
OCR MEI S1 Q2
7 marks Moderate -0.8
2 The lifetimes in hours of 90 components are summarised in the table.
Lifetime \(( x\) hours \()\)\(0 < x \leqslant 20\)\(20 < x \leqslant 30\)\(30 < x \leqslant 50\)\(50 < x \leqslant 65\)\(65 < x \leqslant 100\)
Frequency2413142118
  1. Draw a histogram to illustrate these data.
  2. In which class interval does the median lie? Justify your answer.
OCR MEI S1 Q5
6 marks Easy -1.2
5 The times taken for 480 university students to travel from their accommodation to lectures are summarised below.
Time \(( t\) minutes \()\)\(0 \leqslant t < 5\)\(5 \leqslant t < 10\)\(10 \leqslant t < 20\)\(20 \leqslant t < 30\)\(30 \leqslant t < 40\)\(40 \leqslant t < 60\)
Frequency3415318873275
  1. Illustrate these data by means of a histogram.
  2. Identify the type of skewness of the distribution.
OCR MEI S1 Q6
6 marks Easy -1.2
6 The times taken for 480 university students to travel from their accommodation to lectures are summarised below.
Time \(( t\) minutes \()\)\(0 \leqslant t < 5\)\(5 \leqslant t < 10\)\(10 \leqslant t < 20\)\(20 \leqslant t < 30\)\(30 \leqslant t < 40\)\(40 \leqslant t < 60\)
Frequency3415318873275
  1. Illustrate these data by means of a histogram.
  2. Identify the type of skewness of the distribution.
OCR MEI S1 2010 June Q3
7 marks Moderate -0.8
3 The lifetimes in hours of 90 components are summarised in the table.
Lifetime \(( x\) hours \()\)\(0 < x \leqslant 20\)\(20 < x \leqslant 30\)\(30 < x \leqslant 50\)\(50 < x \leqslant 65\)\(65 < x \leqslant 100\)
Frequency2413142118
  1. Draw a histogram to illustrate these data.
  2. In which class interval does the median lie? Justify your answer.
Edexcel S1 2024 October Q5
Moderate -0.3
5.
\includegraphics[max width=\textwidth, alt={}]{fe416f2e-bc81-444b-a0ca-f0eae9a8b149-16_990_1473_246_296}
The histogram shows the number of hours worked in a given week by a group of 64 freelance photographers.
  1. Give a reason to justify the use of a histogram to represent these data. Given that 16 of these freelance photographers spent between 10 and 20 hours working in this week,
  2. estimate the number that spent between 12 and 24 hours working in this week.
  3. Find an estimate for the median time spent working in this week by these 64 freelance photographers. Charlie decides to model these data using a normal distribution. Charlie calculates an estimate of the mean to be 23.9 hours to one decimal place.
  4. Comment on Charlie's decision to use a normal distribution. Give a justification for your answer.
WJEC Unit 2 2022 June Q2
Standard +0.3
The probability distribution for \(X\), the lifetime of a light bulb, in hours, is given below.
\(X\)\(256 \leqslant x < 259\)\(259 \leqslant x < 262\)\(262 \leqslant x < 265\)\(265 \leqslant x < 267\)\(267 \leqslant x < 300\)
Probability0.050.250.450.200.05
a) Suppose that a random sample of 40 light bulbs is tested, and a histogram is drawn of their lifetimes. Calculate the expected height of the bar for the interval \(262 \leqslant x < 265\).
b) Now suppose that the last two intervals are changed to \(265 \leqslant x < 268\) and \(268 \leqslant x < 300\). Explain why it is not possible to tell what will happen to the expected heights of the last two bars.
c) Celyn collects a different random sample of 40 light bulbs to test. She draws a histogram of their lifetimes and finds that it is different to the histogram referred to in part (a). Should Celyn be concerned that the two histograms are different?