Using Summary Statistics (Edexcel GCSE Statistics: Higher)

Sophie has been researching the weights of fish caught at a fishing competition.

The table below gives information about the weights, in kg, of two types of fish that were caught, bass and mackerel.

Compare, in context, the distribution of the weights of bass and mackerel.

Explain when it would be more appropriate to use the median rather than the mean in describing a distribution.

Mateo investigated the heights of male and female giraffes.

Using secondary data, he recorded the height, in metres, of each female in a sample of 20 female giraffes and the height, in metres, of each male in a sample of 20 male giraffes.

The box plots for both samples are shown below.

Compare the two distributions of heights.

Give three comparisons and interpret one of your comparisons.

The levels of nitrogen in various soil samples is being investigated.

Several soil samples were taken and the level of nitrogen, in mg/kg, was recorded. Summary statistics were calculated and these are shown in the table below.

Calculate the skew for the distribution of nitrogen levels in the soil and interpret this value in context.

Give your answer 2 decimal places.

In order to qualify to take part in an international sports competition, each athlete must first complete a trial long jump.

The table gives information about the results of the greatest distance, in metres, achieved by all athletes.

To be selected for the competition, an athlete must achieve a standardised score of at least 1.8 for the jump.

Santiago manages to jump a distance of 8.1 m.

Determine whether or not Santiago will be selected for the team.

Christopher's standardised score for his jump is -0.9

Ruben's standardised score for his jump is -1.5

Compare Christopher's jump with Ruben's jump.

Give a reason for your answer.

The table gives the standardised scores for Anna in three subject tests.

Use the standardised scores to compare Anna's results relative to the other students in each of the three subject tests.

Give reasons for your comparisons.

The raw score for each test is also known.

Each test has the same maximum raw score.

Explain why it is appropriate to use standardised scores rather than raw scores to compare performance.

The table below shows Anna's standardised score for her Geography test.

It also shows the mean and standard deviation of the scores awarded to the other students who also took the test.

Work out Anna's raw score for Geography.

Give your answer to the nearest whole number.

Solomon collected the weights, in kg, of a group of rabbits.

He uses statistical software to calculate the following summary statistics.

Calculate the skew for the distribution of weights and interpret this value in the context of Solomon's data

Nellie takes part in two cycling races. She is particularly interested in analysing her performance against other competitors.

The table below gives Nellie's times to complete each of the races. It also gives the mean and standard deviation of the times for each of the two races for all competitors who took part.

Nellie concludes that because she completed the second race faster than the first race she performed better in the second race as compared to the other candidates.

Use statistical calculations to assess Nellie's conclusion.

Leila collects information about the tail lengths of 40 pet cats. She records her results in the grouped frequency table shown below.

Leila gives the grouped frequency table to her friend Alannah and asks her to use the information to work out an estimate of the standard deviation of the lengths of the cat tails.

Explain why Alannah can only work out an estimate of the standard deviation.

Alannah uses the information in the table to work out the following estimates of the summary statistics

          and          

Using Alannah's estimates of the summary statistics, calculate an estimate of the skew of the distribution of the lengths of the 40 cat tails.

Give your answer to 2 decimal places.

Interpret your answer to part (b) in the context of the data in the table.