2.2 Data Presentation

A teacher took 19 students on an international trip. The incomplete box plot below shows part of the summary of the weights, in kg, of the luggage brought by each student. Each student's luggage weighed a different value.

The median weight is 4 kg more than the lower quartile. The range of weights is three times the interquartile range of weights.

Use the information above to complete the box plot.

Calculate the proportion of weights which were less than the 20 kg.

Remy is timing how long it takes each of his 80 rats to find the exit to a maze.  Every two and a half minutes he records the number of rats which have found the exit which he then represents as a cumulative frequency curve.

Based on the graph, write down an inequality for the time, t, taken by the fastest rat.  

Remy’s assistant also recorded the actual times taken by the fastest and slowest rats.  She has used this information to begin constructing a box plot to represent the data.

Use the cumulative frequency curve to complete the box plot for the times.

An annual cheese-rolling contest involves participants chasing a 4 kg round of cheese down a steep 200 yard long hillside.  A group of 60 friends participated in the contest and the table below summarises the distances travelled by each before first falling over.

How many of the 60 friends made it to the bottom without falling over?

Draw a cumulative frequency graph for the information in the table.

The steepest part of the hill is between 100 and 140 yards away from the start. Using your graph, estimate how many people fell during this section of the hill.

The histogram below shows the masses, in grams, of 80 apples.

Find estimates for the median, lower quartile and upper quartile.

Given that the lightest apple weighs 41 g and that the range of masses is 97 g, draw a box plot to show the distribution of the masses of the apples.

Aggie is using the large data set to learn about the mean age of residents from different local authorities in 2011. She takes a random sample of 19 local authorities. The mean ages for those local authorities are listed below:

35          35.7          36.2          36.2
37.4       37.4          38.4          40
40          40             40.5          40.7
40.9       41             41.3          41.5
41.6       42.6          43.9          

On the grid below draw a box plot for the information above.

Aggie discovers that the value 35.7 is incorrect. Aggie corrects the value and redraws the box plot.

Given that the box plot is unchanged, write down a range of values for the correct value . 

120 competitors enter an elimination race for charity.  Runners set off from the same start running as many laps of the course as possible.  Their total distance is tracked and the competitor who runs the furthest over a 6-hour period is the winner.  The distances runners achieved are recorded in the table below:

On the grid below, draw a cumulative frequency graph for the information in the table.

Use your graph to find an estimate for the median and interquartile range.

The total amount of time cleaners spent dealing with unplanned incidents in a supermarket was recorded each day.  Data collected over 49 days is summarised in the table below.

On the grid below, draw a histogram to represent this data.

Estimate how often cleaners spent longer than 3 hours dealing with incidents.

A taxi firm, JustDrive, records data on the amount of time, to the nearest minute, that customers had to wait before their taxis arrived.  A random sample of 20 times is given below:

Find the median and interquartile range of the waiting times.

On the grid, draw a box plot for the information given above.

Filmworld cinemas collected data on the ages of visitors to their cinemas during a 24-hour period.  The incomplete histogram and frequency table show some of the information they collected:

Use the information to complete the histogram and fill out the missing data in the frequency table.

Police check the speed of vehicles travelling along a stretch of highway.  The cumulative frequency curve below summarises the data for the speeds, in kmph, of 80 vehicles:

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

The speed limit for this section of road is 80 kmph.

Vehicles travelling above the speed limit are issued with a speeding ticket.  Those travelling more than 10% over the speed limit are pulled over.  Use the graph to estimate the percentage of vehicles that the police pull over.