Cumulative Frequency & Box Plots (CIE IGCSE Maths: Extended)

Gemma records the times, in seconds, taken for a group of children and a group of adults to complete a puzzle.
The box-and-whisker plot shows information about the times taken for the children to complete the puzzle.

Find the interquartile range of the times taken for the children to complete the puzzle.

.................................... seconds

The table shows some information about the times, in seconds, taken for the adults to complete the puzzle.

On the grid above, draw the box-and-whisker plot for the adults.

160 students record the amount of time, hours, they each spend playing computer games in a week.
This information is shown in the cumulative frequency diagram.

Use the diagram to find an estimate of

Use the diagram to complete this frequency table.

The time,  minutes, 80 students each spend completing their homework is recorded.
The cumulative frequency diagram shows the results.

Use the cumulative frequency diagram to find an estimate of the median.
 

......................................... min

Use the cumulative frequency diagram to find an estimate of the interquartile range.
 

......................................... min

Use the cumulative frequency diagram to find an estimate of the number of students who spend more than 40 minutes completing their homework.

The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework.


Use the cumulative frequency diagram to find an estimate of the interquartile range.

......................................min

Use the cumulative frequency diagram to find an estimate of the number of students who took more than 50 minutes to complete the homework.

The table gives some information about the heights of 80 girls.

Draw a box plot to represent this information.

Work out an estimate for the number of these girls with a height between 133 cm and 157 cm.

The table shows information about the speeds of lorries.

Speed () in km/h	Frequency

Complete the cumulative frequency table for this information.

Speed () in km/h	Cumulative frequency

On the grid, draw a cumulative frequency graph for your table.

Find an estimate for the number of lorries with a speed of more than km/h.

These box-and-whisker plots show the monthly electricity costs for 100 different households who use Electro company or Spark company.

Tom says that the monthly costs with Electro company are lower and vary less than with Spark company.

Is Tom correct?
Justify your answer with reference to the box-and-whisker plots.

Harry grows tomatoes.
This year he put his tomato plants into two groups, group A and group B.

Harry gave fertiliser to the tomato plants in group A.
He did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group A.
The cumulative frequency graph shows some information about these weights.

Use the graph to find an estimate for the median weight.

The 60 tomatoes from group A
   had a minimum weight of 153 grams
   and a maximum weight of 186 grams.

Use this information and the cumulative frequency graph to draw a box plot for the 60 tomatoes from group A.

Harry did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group B.
He drew this box plot for his results.

Compare the distribution of the weights of the tomatoes from group A with the distribution of the weights of the tomatoes from group B.

The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres.

Use the graph to find an estimate for the median time.

A swimmer has to swim 50 metres in 60 seconds or less to qualify for the swimming team.

The team captain says,

   "More than 25% of swimmers have qualified for the swimming team."

Is the team captain right?
You must show how you got your answer.

For these 80 swimmers

   the least time taken was 28 seconds
   and the greatest time taken was 96 seconds.

Use the cumulative frequency graph and the information above to draw a box plot for the times taken by the swimmers.

The cumulative frequency graphs show information about the times taken by 100 male runners and by 100 female runners to finish the London marathon. 

A male runner is chosen at random.

Find an estimate for the probability that this runner took less than 4 hours to finish the London marathon.

Use medians and interquartile ranges to compare the distribution of the times taken by the male runners with the distribution of the times taken by the female runners.

The cumulative frequency graph gives information about the weights, in grams, of 90 bags of sweets.

Roberto sells the bags of sweets to raise money for charity.
Bags with a weight greater than grams are labelled large bags and sold for 3.75 euros each bag.

The total amount of money he receives by selling all the large bags is 93.75 euros.

Find the value of .