Representation of Data

On the grid below, draw a cumulative frequency graph to illustrate this information.

38% of these leaves are of length $k$ cm or more.

Use your graph to find an estimate for $k$.

Calculate an estimate for the mean length of these 250 leaves.

Draw a back-to-back stem-and-leaf diagram to represent this information, with Gulls on the left-hand side.

Find the median and the interquartile range of the times of the runners from the Gulls.

Two other teams of runners, the Eagles and the Swifts, also took part in the event. The recorded times in seconds for 20 runners from the Eagles and 30 runners from the Swifts are denoted by $x$ and $y$ respectively.

It is given that $\sum x = 175.0$ and that the mean of $y$ is $8.4$.

Find the mean of the times taken by all 50 runners.

It is given that $\sum x^2 = 1823.0$.

It is also known that the standard deviation of the times taken by all 50 runners is $1.38$ seconds.

Find the value of $\sum y^2$, correct to 1 decimal place.

On the grid, draw a cumulative frequency graph to illustrate this information.

120 students take more than $k$ minutes to travel to college. Use your graph to estimate the value of $k$.

Calculate estimates of the mean and standard deviation of the times taken to travel to college by the 300 students.

Given that the mean of these 40 values is 124.0, find the value of $k$.

Find the standard deviation of these 40 values of $x$.

Use the graph to estimate how many people took between 4 and 7.5 minutes to complete the puzzle.

On the grid below, draw a box-and-whisker plot to summarise the information in the cumulative frequency graph.

Represent this information in a back-to-back stem-and-leaf diagram with Smarts on the left-hand side.

For the Teasers, the values of the lower quartile, median and upper quartile are 18, 25 and 37 minutes respectively.

On a single diagram draw box-and-whisker plots for the two teams.

Make two comparisons between the times for the two teams.

Find the median and interquartile range for the annual salaries of employees at Browns.

The annual salary of an employee at Browns is denoted by $x$ thousand dollars and the annual salary of an employee at Greens is denoted by $y$ thousand dollars. It is given that, for the 27 employees at each of the companies,

Find the mean and standard deviation of the annual salaries of these 54 employees.

Draw a histogram to represent this information.

Calculate an estimate of the mean time taken by the 240 competitors.

Draw a back-to-back stem-and-leaf diagram to represent this information, with Linnets on the left-hand side.

Find the interquartile range of the times taken by the Linnets.

On the grid below, draw a box-and-whisker plot to represent the information for the Linnets and the Puffins.

Make one comparison between the times taken by the Linnets and the times taken by the Puffins.

Draw a back-to-back stem-and-leaf diagram to represent the heights of the players from Pelicans and Swans, with Pelicans on the left-hand side.

Find the median and the interquartile range of the heights of the Pelicans.

For the Swans, the lower quartile of the heights is 165 cm, the median is 174 cm and the upper quartile is 181 cm.

Represent the data shown in the back-to-back stem-and-leaf diagram by a pair of box-and-whisker plots in a single diagram.

Make one comparison between the heights of the Pelicans players and the heights of the Swans players.