Measures of Dispersion (Edexcel GCSE Statistics: Higher)

Rhiannon is investigating how many eggs a chicken lays in one month. She recorded the total number of eggs that each chicken from a group laid in June.

Rhiannon worked out the summary statistics for the number of eggs that were laid by the chickens.

Lower quartile = 23
Median = 26
Upper quartile = 28

One chicken laid only 16 eggs.

Determine whether or not the number of eggs that this chicken laid is an outlier.

The table below shows some of the expected percentile heights of boys and girls from 12 to 16 years old.

(Source: World Health Organisation)

Eliza says,

"An estimate of the expected 65th percentile for a girl aged 13 is 161.3 cm"

Explain why this is not a good estimate.

Compare the expected 5th to the 95th percentile range for 14 year old girls with the expected 5th to the 95th percentile range for 14 year old boys.

You must show your working.

Give an interpretation of your comparison in part (b).

Boris wants to investigate the heights of baboons.

The table shows information, in cm, of a sample of 42 adolescent baboons and 35 adult baboons.

Work out the number of adult baboons that have a height greater than 80.9 cm.

The cumulative frequency curve shows information about the times taken by a number of runners to complete a 400 metre race.

Find the 20th to 90th percentile range for this information.

The box plots below give information about the distributions of systolic blood pressure, in mmHg, for two groups of patients with high blood pressure.

The two groups of patients are taking part in a trial of new medication to reduce blood pressure. The first group are taking the new medication, and the second group are not taking the new medication.

Justify, by calculation, that 139 is an outlier for the group taking the new medication.

Jacob collects information about the wingspan, in centimetres, of some emperor penguins and displays his results in a grouped frequency table.

He then calculates the following summary statistics for the information in the table.

where the values of are the class midpoints.

Show that an estimate of the standard deviation of the wingspan of emperor penguins is

You may use Jacob's summary statistics.

Nils asked 60 students in his school to throw a basketball into a bucket from a set distance as many times as they could in 1 minute.

He recorded the number of times they managed to successfully throw the ball into the bucket. Nils then created a spreadsheet and sorted the data in descending order of size.

Part of the spreadsheet is shown below.

Nils finds the summary statistics of the data using statistical software.

The results are shown below.

Using the information in the table and the spreadsheet, draw a box plot with any outliers clearly marked.

You must show any calculations you use.

A researcher is investigating the resting heart rates, in beats per minute, of a group of adults.

The histogram and grouped frequency table below give information about the resting heart rates of these adults.

The researcher calculated the summary statistics for the data using statistical software.

By calculating limits for outliers using the mean and the standard deviation, explain whether or not there could be any outliers in the data.