Complete frequency table from histogram only

Questions that provide a histogram and ask students to construct or complete a frequency table by reading frequency densities and calculating frequencies from the histogram bars.

8 questions

CAIE S1 2017 June Q7
7 The following histogram represents the lengths of worms in a garden.
\includegraphics[max width=\textwidth, alt={}, center]{67412184-38f6-4b37-afe3-4a149a2e0586-10_789_1195_301_466}
  1. Calculate the frequencies represented by each of the four histogram columns.
  2. On the grid on the next page, draw a cumulative frequency graph to represent the lengths of worms in the garden.
    \includegraphics[max width=\textwidth, alt={}, center]{67412184-38f6-4b37-afe3-4a149a2e0586-11_1111_1409_251_408}
  3. Use your graph to estimate the median and interquartile range of the lengths of worms in the garden.
  4. Calculate an estimate of the mean length of worms in the garden.
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CAIE S1 2010 November Q5
5 The following histogram illustrates the distribution of times, in minutes, that some students spent taking a shower.
\includegraphics[max width=\textwidth, alt={}, center]{ec425eaf-8afc-4671-9ef3-ba2477b884ef-3_1031_1326_372_406}
  1. Copy and complete the following frequency table for the data.
    Time \(( t\) minutes \()\)\(2 < t \leqslant 4\)\(4 < t \leqslant 6\)\(6 < t \leqslant 7\)\(7 < t \leqslant 8\)\(8 < t \leqslant 10\)\(10 < t \leqslant 16\)
    Frequency
  2. Calculate an estimate of the mean time to take a shower.
  3. Two of these students are chosen at random. Find the probability that exactly one takes between 7 and 10 minutes to take a shower.
OCR MEI S1 2007 June Q2
2 The histogram shows the amount of money, in pounds, spent by the customers at a supermarket on a particular day.
\includegraphics[max width=\textwidth, alt={}, center]{5e4f3310-b96e-43db-9b6d-61da3270db06-2_977_1132_808_340}
□ represents 20 customers
  1. Express the data in the form of a grouped frequency table.
  2. Use your table to estimate the total amount of money spent by customers on that day.
OCR MEI S1 Q2
2 The histogram shows the amount of money, in pounds, spent by the customers at a supermarket on a particular day.
\includegraphics[max width=\textwidth, alt={}, center]{c7cb0f6b-7b6b-4c52-8287-7efc6bd70247-2_985_1473_470_379}
  1. Express the data in the form of a grouped frequency table.
  2. Use your table to estimate the total amount of money spent by customers on that day.
Edexcel S1 2023 January Q1
  1. The histogram shows the times taken, \(t\) minutes, by each of 100 people to swim 500 metres.
    \includegraphics[max width=\textwidth, alt={}, center]{c316fa29-dedc-4890-bd82-31eb0bb819f9-02_986_1070_342_424}
    1. Use the histogram to complete the frequency table for the times taken by the 100 people to swim 500 metres.
    Time taken ( \(\boldsymbol { t }\) minutes)\(5 - 10\)\(10 - 14\)\(14 - 18\)\(18 - 25\)\(25 - 40\)
    Frequency ( \(\boldsymbol { f }\) )101624
  2. Estimate the number of people who took less than 16 minutes to swim 500 metres.
  3. Find an estimate for the mean time taken to swim 500 metres. Given that \(\sum f t ^ { 2 } = 41033\)
  4. find an estimate for the standard deviation of the times taken to swim 500 metres. Given that \(Q _ { 3 } = 23\)
  5. use linear interpolation to estimate the interquartile range of the times taken to swim 500 metres.
Edexcel S1 2024 January Q1
  1. The histogram below shows the distribution of the heights, to the nearest cm , of 408 plants.
    \includegraphics[max width=\textwidth, alt={}, center]{86446ce3-496a-4f02-9566-9b207bac9efa-02_1001_1473_340_296}
    1. Use the histogram to complete the following table.
    Height \(( h\) cm)\(5 \leqslant h < 9\)\(9 \leqslant h < 13\)\(13 \leqslant h < 15\)\(15 \leqslant h < 17\)\(17 \leqslant h < 25\)
    Frequency32152120
  2. Use interpolation to estimate the median. The mean height of these plants is 13.2 cm correct to one decimal place.
  3. Describe the skew of these data. Give a reason for your answer. Two of these plants are chosen at random.
  4. Estimate the probability that both of their heights are between 8 cm and 14 cm
Edexcel S1 2012 January Q1
  1. The histogram in Figure 1 shows the time, to the nearest minute, that a random sample of 100 motorists were delayed by roadworks on a stretch of motorway.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bc8ef6c7-a321-4ecf-962d-f469a95fc8c8-02_1312_673_349_639} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure}
  1. Complete the table.
    Delay (minutes)Number of motorists
    4-66
    7-8
    921
    10-1245
    13-159
    16-20
  2. Estimate the number of motorists who were delayed between 8.5 and 13.5 minutes by the roadworks.
Edexcel S1 2007 June Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{045e10d2-1766-4399-aa0a-5619dd0cce0f-10_726_1509_255_278} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a histogram for the variable \(t\) which represents the time taken, in minutes, by a group of people to swim 500 m .
  1. Complete the frequency table for \(t\).
    \(t\)\(5 - 10\)\(10 - 14\)\(14 - 18\)\(18 - 25\)\(25 - 40\)
    Frequency101624
  2. Estimate the number of people who took longer than 20 minutes to swim 500 m .
  3. Find an estimate of the mean time taken.
  4. Find an estimate for the standard deviation of \(t\).
  5. Find the median and quartiles for \(t\). One measure of skewness is found using \(\frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } }\).
  6. Evaluate this measure and describe the skewness of these data.