Draw histogram from frequency table

The question provides a frequency table with unequal class widths and explicitly asks the student to draw a histogram, with no additional statistical calculations required beyond the histogram construction itself.

10 questions · Easy -1.3

Sort by: Default | Easiest first | Hardest first
CAIE S1 2017 June Q4
6 marks Easy -1.2
4 The times taken, \(t\) seconds, by 1140 people to solve a puzzle are summarised in the table.
Time \(( t\) seconds \()\)\(0 \leqslant t < 20\)\(20 \leqslant t < 40\)\(40 \leqslant t < 60\)\(60 \leqslant t < 100\)\(100 \leqslant t < 140\)
Number of people320280220220100
  1. On the grid, draw a histogram to illustrate this information. \includegraphics[max width=\textwidth, alt={}, center]{7652f36c-59b5-4fcd-b17b-d796dc82aec0-05_812_1406_804_411}
  2. Calculate an estimate of the mean of \(t\).
CAIE S1 2003 November Q2
4 marks Easy -1.3
2 The floor areas, \(x \mathrm {~m} ^ { 2 }\), of 20 factories are as follows.
150350450578595644722798802904
1000133015331561177819602167233024333231
Represent these data by a histogram on graph paper, using intervals $$0 \leqslant x < 500,500 \leqslant x < 1000,1000 \leqslant x < 2000,2000 \leqslant x < 3000,3000 \leqslant x < 4000 .$$
CAIE S1 2016 November Q5
9 marks Moderate -0.8
5 The number of people a football stadium can hold is called the 'capacity'. The capacities of 130 football stadiums in the UK, to the nearest thousand, are summarised in the table.
Capacity\(3000 - 7000\)\(8000 - 12000\)\(13000 - 22000\)\(23000 - 42000\)\(43000 - 82000\)
Number of stadiums403018348
  1. On graph paper, draw a histogram to represent this information. Use a scale of 2 cm for a capacity of 10000 on the horizontal axis.
  2. Calculate an estimate of the mean capacity of these 130 stadiums.
  3. Find which class in the table contains the median and which contains the lower quartile.
OCR MEI S1 2005 January Q1
7 marks Easy -1.8
1 The number of minutes of recorded music on a sample of 100 CDs is summarised below.
Time ( \(t\) minutes)\(40 \leqslant t < 45\)\(45 \leqslant t < 50\)\(50 \leqslant t < 60\)\(60 \leqslant t < 70\)\(70 \leqslant t < 90\)
Number of CDs261831169
  1. Illustrate the data by means of a histogram.
  2. Identify two features of the distribution.
OCR MEI S1 2007 January Q3
6 marks Easy -1.8
3 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 Q2
18 marks Moderate -0.8
2 The engine sizes \(x \mathrm {~cm} ^ { 3 }\) of a sample of 80 cars are summarised in the table below.
Engine size \(x\)\(500 \leqslant x \leqslant 1000\)\(1000 < x \leqslant 1500\)\(1500 < x \leqslant 2000\)\(2000 < x \leqslant 3000\)\(3000 < x \leqslant 5000\)
Frequency72226187
  1. Draw a histogram to illustrate the distribution.
  2. A student claims that the midrange is \(2750 \mathrm {~cm} ^ { 3 }\). Discuss briefly whether he is likely to be correct.
  3. Calculate estimates of the mean and standard deviation of the engine sizes. Explain why your answers are only estimates.
  4. Hence investigate whether there are any outliers in the sample.
  5. A vehicle duty of \(\pounds 1000\) is proposed for all new cars with engine size greater than \(2000 \mathrm {~cm} ^ { 3 }\). Assuming that this sample of cars is representative of all new cars in Britain and that there are 2.5 million new cars registered in Britain each year, calculate an estimate of the total amount of money that this vehicle duty would raise in one year.
  6. Why in practice might your estimate in part (v) turn out to be too high?
Edexcel S1 2003 January Q1
4 marks Easy -1.3
  1. The total amount of time a secretary spent on the telephone in a working day was recorded to the nearest minute. The data collected over 40 days are summarised in the table below.
Time (mins)\(90 - 139\)\(140 - 149\)\(150 - 159\)\(160 - 169\)\(170 - 179\)\(180 - 229\)
No. of days81010444
Draw a histogram to illustrate these data
Edexcel S1 2004 November Q7
6 marks Easy -1.8
7. A college organised a 'fun run'. The times, to the nearest minute, of a random sample of 100 students who took part are summarised in the table below.
TimeNumber of students
\(40 - 44\)10
\(45 - 47\)15
4823
\(49 - 51\)21
\(52 - 55\)16
\(56 - 60\)15
  1. Give a reason to support the use of a histogram to represent these data.
  2. Write down the upper class boundary and the lower class boundary of the class 40-44.
  3. On graph paper, draw a histogram to represent these data. END
Edexcel S1 2003 June Q1
5 marks Easy -1.8
  1. In a particular week, a dentist treats 100 patients. The length of time, to the nearest minute, for each patient's treatment is summarised in the table below.
Time
(minutes)
\(4 - 7\)8\(9 - 10\)11\(12 - 16\)\(17 - 20\)
Number
of
patients
122018221513
Draw a histogram to illustrate these data.
Edexcel S1 2002 January Q2
7 marks Moderate -0.8
A meteorologist measured the number of hours of sunshine, to the nearest hour, each day for 100 days. The results are summarised in the table below.
Hours of sunshineDays
116
2-432
5-628
712
89
9-112
121
  1. On graph paper, draw a histogram to represent these data. [5]
  2. Calculate an estimate of the number of days that had between 6 and 9 hours of sunshine. [2]