Histograms and cumulative frequency graphs Problem set B

Draw a histogram for each set of data.

1. (a) The times taken by 50 pupils to solve a puzzle: 0–3 min: 5, 3–6 min: 12, 6–9 min: 17, 9–12 min: 11, 12–15 min: 5.
2. (b) The ages of 60 people at a sports club: 10–15 years: 9, 15–20 years: 21, 20–30 years: 20, 30–50 years: 10.

The histogram shows the lengths of 80 fish.

1. (a) Estimate the number of fish shorter than 14 cm.
2. (b) Estimate the number of fish between 17 and 26 cm long.

The table shows the heights of 50 plants.

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

The graph shows the journey times of 40 commuters.

1. (a) Estimate the median.
2. (b) Estimate the interquartile range.
3. (c) Estimate the 90th percentile.
4. (d) Estimate how many commuters were less than 30 minutes.
5. (e) Estimate the percentage of commuters that were more than 50 minutes.

The numbers of goals scored by 12 teams in a season were: 31, 24, 28, 35, 40, 27, 33, 38, 29, 36, 25, 32.

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 lengths, in centimetres, of 10 leaves were: 45, 52, 3, 41, 48, 44, 38, 50, 42, 47.

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 15, second smallest 19, lower quartile 30, median 38, upper quartile 46, second largest 57, largest 82.

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 lengths of the fish caught in a competition.

1. (a) How many were measured?
2. (b) Estimate the number between 36 and 55 cm.
3. (c) Estimate this as a percentage of the total.

The histogram shows the times, in minutes, that 60 customers spent in a shop.

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

The cumulative frequency table shows the ages, in years, of 80 people on a bus.

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

The graph shows the masses, in grams, of 80 eggs.

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

The table shows the times, in minutes, that 60 pupils took to cycle to school (group A). For group B the five-number summary was 15, 28, 41, 52, 60.

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 masses (in grams) of 50 items. Graphs A, B and C are the cumulative frequency graphs of the same data. Match each histogram to its graph. Histogram 1: frequencies 5, 12, 18, 10, 5 for classes 0–20, 20–40, 40–60, 60–80, 80–100. Histogram 2: frequencies 20, 14, 9, 5, 2 for classes 0–20, 20–40, 40–60, 60–80, 80–100. Histogram 3: frequencies 2, 5, 9, 14, 20 for classes 0–20, 20–40, 40–60, 60–80, 80–100.

The diagram shows three cumulative frequency graphs, A, B and C, for the lengths (in centimetres) of three batches of 80 plants. 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, 25, 33, 38, 50; Box plot Q: 0, 20, 25, 30, 50; Box plot R: 0, 12, 17, 25, 50.