Histograms and cumulative frequency graphs Problem set A

Draw a histogram for each set of data.

1. (a) The masses of 40 parcels: 0–5 kg: 4, 5–10 kg: 9, 10–15 kg: 15, 15–20 kg: 8, 20–25 kg: 4.
2. (b) The lengths of 70 journeys: 0–5 km: 10, 5–10 km: 15, 10–20 km: 24, 20–40 km: 21.

The histogram shows the lengths of 60 phone calls.

1. (a) Estimate the number of calls shorter than 7 minutes.
2. (b) Estimate the number of calls between 12 and 22 minutes long.

The table shows the lengths of 40 trout.

1. (a) Complete a cumulative frequency table.
2. (b) Draw the cumulative frequency graph.

The graph shows the masses of 50 potatoes.

1. (a) Estimate the median.
2. (b) Estimate the interquartile range.
3. (c) Estimate the 90th percentile.
4. (d) Estimate how many potatoes were less than 20 g.
5. (e) Estimate the percentage of potatoes that were more than 40 g.

The scores of 11 players in a game were: 14, 22, 9, 17, 25, 19, 12, 21, 16, 28, 18.

1. (a) Find the median and the quartiles.
2. (b) Find the interquartile range.
3. (c) Show that there are no outliers, and draw a box plot.

The waiting times, in minutes, of 11 buses were: 7, 9, 8, 13, 5, 31, 10, 12, 8, 14, 11.

1. (a) Find the median, the quartiles and the interquartile range.
2. (b) Test whether there are any outliers.
3. (c) Draw a box plot.

A data set has: smallest value 4, second smallest 18, lower quartile 24, median 29, upper quartile 35, second largest 50, largest 71.

1. (a) Determine whether the data set has any outliers.
2. (b) State where the whiskers of the box plot end.

The histogram shows the ages of the visitors to a library one day.

1. (a) How many were measured?
2. (b) Estimate the number between 25 and 45 years.
3. (c) Estimate this as a percentage of the total.

The histogram shows the distances, in metres, that 100 children threw a ball.

1. (a) Write the data as a grouped frequency table.
2. (b) Estimate the mean.

The cumulative frequency table shows the times, in seconds, that 100 students took to solve a puzzle.

1. (a) Draw a histogram of the data.
2. (b) Estimate the mean.

The graph shows the time, in minutes, that 60 students spent reading last night.

1. (a) Estimate the median.
2. (b) Estimate the lower and upper quartiles.
3. (c) Draw a box plot.

The table shows the hours 40 students spent revising in one week (group A). For group B the five-number summary was 5, 22, 30, 41, 50.

1. (a) Complete a cumulative frequency table and draw the graph.
2. (b) Estimate the median and the quartiles.
3. (c) Draw a box plot for the data.
4. (d) Compare the two groups. Refer to the median and the interquartile range.

Three histograms show the times (in minutes) for 40 people. Graphs A, B and C are the cumulative frequency graphs of the same data. Match each histogram to its graph. Histogram 1: frequencies 4, 9, 14, 9, 4 for classes 0–10, 10–20, 20–30, 30–40, 40–50. Histogram 2: frequencies 16, 11, 7, 4, 2 for classes 0–10, 10–20, 20–30, 30–40, 40–50. Histogram 3: frequencies 2, 4, 7, 11, 16 for classes 0–10, 10–20, 20–30, 30–40, 40–50.

The diagram shows three cumulative frequency graphs, A, B and C, for the times (in minutes) of three groups of 60 people. Three box plots P, Q and R show the same data in some order. Match each box plot to its graph. The five-number summaries are: Box plot P: 0, 12, 18, 30, 60; Box plot Q: 0, 30, 42, 48, 60; Box plot R: 0, 27, 35, 43, 60.