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19.5 Comparing distributions and drawing conclusions

19.5 Comparing distributions and drawing conclusions

You can compare two or more sets of data by looking at the distribution of the data.
To do this, you draw graphs to show the distributions, then look for di%erences between the graph.
You can also work out statistics such as the mean, median, mode and range, and use these values to
compare the distributions.

Worked example 19.5

a A gardener plants two different types of daffodil bulb. When Height of daffodils
they are fully grown he measures the heights of the daffodils. 20 Type A Type B
The frequency polygons show the heights of the two different
types of daffodils. 15
Look at the shape of the distributions. Write three sentences Frequency 10
to compare the heights of the two different types of daffodil. 5
b Sally wants to buy a holiday apartment in Malaga or Madrid. 0 0 10 20 30 40 50
The table shows the average monthly maximum temperatures Height (cm)
in Malaga and Madrid.

Average monthly maximum temperatures (°C)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Malaga 17 17 19 20 23 27 29 30 28 24 20 17

Madrid 11 12 16 17 22 28 32 32 28 20 14 11
Sally decides to buy an apartment in Malaga because she says that, on average, the temperatures are
higher and more consistent than in Madrid. Has Sally made the right decision? Explain your answer.

a The heights of the type B daffodils are more varied. When you compare frequency polygons,
Six more of the type B daffodils than the type A look at the width, or spread, of the data to
daffodils reached the greatest height of 40–50 cm. see which set of values is more varied. Also
All of the type A daffodils grew taller than 10 cm, compare specific height intervals, and give
whereas four of the type B daffodils were below numerical comparisons to show that you
10 cm in height. fully understand the graphs.

b Mean Median Mode Range Sally is talking about averages, which means
you need to work out the mean, median and
Malaga 22.6 °C 21.5 °C 17 °C 13 °C mode. She also mentions consistency, which
Madrid 20.3 °C 18.5 °C none 21 °C means you need to work out the range.
Once you have worked out the averages and
The mean and median temperatures for Malaga are ranges, present your results in a table. You
both higher than those for Madrid so, on average, can then use the data in the table to make
Malaga is warmer. It is not possible to compare the comparisons. Make sure you explain clearly
modes as Madrid does not have one. The range for the decisions you have taken.
Malaga is lower than that for Madrid, which means
that the temperatures are more consistent. So Sally
is correct and has made the right decision.

186 19 Interpreting and discussing results