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Data Variability Measures

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Data Variability Measures

Show calculations where appropriate. Use a calculator for standard deviation and round answers to 1 decimal place. Unless a question says otherwise, treat each listed data set as the full population.

Range and spread

1.The lengths, in centimetres, of six seedlings are 14, 19, 17, 23, 16 and 21. Find the maximum, the minimum and the range.

2.Two netball teams recorded these points in five games. Team K: 32, 41, 37, 35, 40. Team M: 28, 46, 34, 43, 31. Calculate each team's range. Which team's points were more consistent, based on range? Explain briefly.

3.A data set has a much larger range than another data set measured in the same units. What does this usually tell you?

Its values are more widely spread from lowest to highest.
Its mean must be larger.
It must contain more observations.
Its values are all close to the mean.

Standard deviation

4.The daily number of customers at a small café over five days was 18, 22, 20, 16 and 24. Find the mean and the population standard deviation, to 1 decimal place.

5.Two towns have the same mean monthly rainfall of 90 mm. Town P has a standard deviation of 12 mm and Town Q has a standard deviation of 31 mm. Which town has more variable monthly rainfall? Explain what the standard deviations indicate.

6.Match each standard deviation description to the best interpretation.

A standard deviation close to 0
A large standard deviation
A standard deviation of 0
A smaller standard deviation than a comparison set

Values tend to be widely spread around the mean
Values tend to lie close to the mean
Every value in the data set is identical
The data set has less spread around its mean

Compare and interpret variability

Group

Mean score

Standard deviation

68%

6.4 percentage points

68%

11.7 percentage points

7.Use the summary table to decide which statements are true. Select all that apply.

The two groups have the same mean score.
Group R has less variability in scores than Group S.
Group S has scores that are more spread around its mean.
Group R must have a higher maximum score than Group S.

8.A sports coach records the sprint times, in seconds, of two training groups. Group A: 12.1, 12.3, 12.4, 12.6, 12.6. Group B: 11.7, 12.0, 12.3, 12.7, 13.3. Calculate each range, then state which group has the greater spread according to this measure.

9.Explain one way the range and standard deviation provide different information about a data set, and why looking at both can be useful.