Histogram from continuous grouped data

Questions where the grouped frequency table uses continuous class intervals (e.g., 0 ≤ t < 20, 20 ≤ t < 30) and the histogram is drawn directly from these boundaries.

6 questions

CAIE S1 2022 June Q3
3 The times taken to travel to college by 2500 students are summarised in the table.
Time taken \(( t\) minutes \()\)\(0 \leqslant t < 20\)\(20 \leqslant t < 30\)\(30 \leqslant t < 40\)\(40 \leqslant t < 60\)\(60 \leqslant t < 90\)
Frequency440720920300120
  1. Draw a histogram to represent this information.
    \includegraphics[max width=\textwidth, alt={}, center]{d69f6a47-7c88-46b3-9e8f-07727106e987-04_1201_1198_1050_516} From the data, the estimate of the mean value of \(t\) is 31.44 .
  2. Calculate an estimate of the standard deviation of the times taken to travel to college.
  3. In which class interval does the upper quartile lie?
    It was later discovered that the times taken to travel to college by two students were incorrectly recorded. One student's time was recorded as 15 instead of 5 and the other's time was recorded as 65 instead of 75 .
  4. Without doing any further calculations, state with a reason whether the estimate of the standard deviation in part (b) would be increased, decreased or stay the same.
CAIE S1 2022 November Q4
4 The times taken, in minutes, to complete a word processing task by 250 employees at a particular company are summarised in the table.
Time taken \(( t\) minutes \()\)\(0 \leqslant t < 20\)\(20 \leqslant t < 40\)\(40 \leqslant t < 50\)\(50 \leqslant t < 60\)\(60 \leqslant t < 100\)
Frequency3246965224
  1. Draw a histogram to represent this information.
    \includegraphics[max width=\textwidth, alt={}, center]{3e74785d-5981-480c-a0fd-f43d5d227f2d-06_1201_1198_1050_516} From the data, the estimate of the mean time taken by these 250 employees is 43.2 minutes.
  2. Calculate an estimate for the standard deviation of these times.
CAIE S1 2003 June Q7
7 A random sample of 97 people who own mobile phones was used to collect data on the amount of time they spent per day on their phones. The results are displayed in the table below.
Time spent per
day \(( t\) minutes \()\)
\(0 \leqslant t < 5\)\(5 \leqslant t < 10\)\(10 \leqslant t < 20\)\(20 \leqslant t < 30\)\(30 \leqslant t < 40\)\(40 \leqslant t < 70\)
Number
of people
11203218106
  1. Calculate estimates of the mean and standard deviation of the time spent per day on these mobile phones.
  2. On graph paper, draw a fully labelled histogram to represent the data.
CAIE S1 2020 June Q7
7 The numbers of chocolate bars sold per day in a cinema over a period of 100 days are summarised in the following table.
Number of chocolate bars sold\(1 - 10\)\(11 - 15\)\(16 - 30\)\(31 - 50\)\(51 - 60\)
Number of days182430208
  1. Draw a histogram to represent this information.
    \includegraphics[max width=\textwidth, alt={}, center]{3ada18de-c4f7-4049-9032-46b796be83c3-12_1203_1399_833_415}
  2. What is the greatest possible value of the interquartile range for the data?
  3. Calculate estimates of the mean and standard deviation of the number of chocolate bars sold.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
OCR MEI S1 Q4
4 The weights, \(w\) grams, of a random sample of 60 carrots of variety A are summarised in the table below.
Weight\(30 \leqslant w < 50\)\(50 \leqslant w < 60\)\(60 \leqslant w < 70\)\(70 \leqslant w < 80\)\(80 \leqslant w < 90\)
Frequency111018147
  1. Draw a histogram to illustrate these data.
  2. Calculate estimates of the mean and standard deviation of \(w\).
  3. Use your answers to part (ii) to investigate whether there are any outliers. The weights, \(x\) grams, of a random sample of 50 carrots of variety B are summarised as follows. $$n = 50 \quad \sum x = 3624.5 \quad \sum x ^ { 2 } = 265416$$
  4. Calculate the mean and standard deviation of \(x\).
  5. Compare the central tendency and variation of the weights of varieties A and B .
OCR MEI Paper 2 2019 June Q3
3 Fig. 3 shows the time Lorraine spent in hours, \(t\), answering e-mails during the working day. The data were collected over a number of months. \begin{table}[h]
Time in hours,
\(t\)
\(0 \leqslant t < 1\)\(1 \leqslant t < 2\)\(2 \leqslant t < 3\)\(3 \leqslant t < 4\)\(4 \leqslant t < 6\)\(6 \leqslant t < 8\)
Number of
days
283642312412
\captionsetup{labelformat=empty} \caption{Fig. 3}
\end{table}
  1. Calculate an estimate of the mean time per day that Lorraine spent answering e-mails over this period.
  2. Explain why your answer to part (a) is an estimate. When Lorraine accepted her job, she was told that the mean time per day spent answering e-mails would not be more than 3 hours.
  3. Determine whether, according to the data in Fig. 3, it is possible that the mean time per day Lorraine spends answering e-mails is in fact more than 3 hours.