Complete frequency table and histogram together

Questions that provide both a partially completed histogram AND a partially completed frequency table, requiring students to use information from both to fill in missing values in the table.

4 questions · Moderate -0.4

2.02b Histogram: area represents frequency
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CAIE S1 2014 June Q6
9 marks Moderate -0.3
6 The times taken by 57 athletes to run 100 metres are summarised in the following cumulative frequency table.
Time (seconds)\(< 10.0\)\(< 10.5\)\(< 11.0\)\(< 12.0\)\(< 12.5\)\(< 13.5\)
Cumulative frequency0410404957
  1. State how many athletes ran 100 metres in a time between 10.5 and 11.0 seconds.
  2. Draw a histogram on graph paper to represent the times taken by these athletes to run 100 metres.
  3. Calculate estimates of the mean and variance of the times taken by these athletes.
Edexcel AS Paper 2 2024 June Q3
7 marks Moderate -0.3
  1. Customers in a shop have to queue to pay.
The partially completed table below and partially completed histogram opposite, give information about the time, \(x\) minutes, spent in the queue by each of 112 customers one day.
Time in queue ( \(\boldsymbol { x }\) minutes)Frequency
\(1 - 2\)64
\(2 - 3\)
\(3 - 4\)13
\(4 - 6\)
\(6 - 8\)3
No customer spent less than 1 minute or longer than 8 minutes in the queue.
  1. Complete the table.
  2. Complete the histogram. Ting decides to model the frequency density for these 112 customers by a curve with equation $$y = \frac { k } { x ^ { 2 } } \quad 1 \leqslant x \leqslant 8$$ where \(k\) is a constant.
  3. Find the value of \(k\)
    \includegraphics[max width=\textwidth, alt={}]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-07_1584_1189_285_443}
    Only use this grid if you need to redraw your histogram. \includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-09_1582_1192_367_440} \includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-09_2267_51_307_36}
Edexcel AS Paper 2 2021 November Q2
9 marks Moderate -0.3
  1. The partially completed table and partially completed histogram give information about the ages of passengers on an airline.
There were no passengers aged 90 or over.
Age ( \(x\) years)\(0 \leqslant x < 5\)\(5 \leqslant x < 20\)\(20 \leqslant x < 40\)\(40 \leqslant x < 65\)\(65 \leqslant x < 80\)\(80 \leqslant x < 90\)
Frequency545901
\includegraphics[max width=\textwidth, alt={}, center]{6dfefd72-338f-40be-ac37-aef56bfaccaa-04_1173_1792_721_139}
  1. Complete the histogram.
  2. Use linear interpolation to estimate the median age. An outlier is defined as a value greater than \(Q _ { 3 } + 1.5 \times\) interquartile range.
    Given that \(Q _ { 1 } = 27.3\) and \(Q _ { 3 } = 58.9\)
  3. determine, giving a reason, whether or not the oldest passenger could be considered as an outlier.
    (2)
Edexcel AS Paper 2 Specimen Q2
5 marks Moderate -0.8
  1. The partially completed histogram and the partially completed table show the time, to the nearest minute, that a random sample of motorists was delayed by roadworks on a stretch of motorway. \includegraphics[max width=\textwidth, alt={}, center]{8f3dbcb4-3260-4493-a230-12577b4ed691-04_1227_1465_354_301}
Delay (minutes)Number of motorists
4-66
7-8
917
10-1245
13-159
16-20
Estimate the percentage of these motorists who were delayed by the roadworks for between 8.5 and 13.5 minutes.