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Data Variability Measures

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Data Variability Measures

Compare how spread out data sets are. For calculation questions, use the population standard deviation for the values given and round answers to 2 decimal places.

Understanding variability

Choose the best answer for each question.

1.Two netball teams each average 31 goals per game. What extra information would best help compare how steady their scoring is?

Each team's range or standard deviation of scores
The number of players on each team
The total goals scored by one team only
The highest score from either team

2.A set of delivery times has a minimum of 12 minutes and a maximum of 29 minutes. What does its range describe?

The average delivery time
The difference between the largest and smallest times
The number of deliveries
The most frequent delivery time

3.What does standard deviation summarise about a data set?

How far values typically lie from the mean
The middle value after the data are ordered
The sum of all the values
How many values are above the median

4.Two data sets have the same mean. One has a smaller standard deviation. What does this usually indicate?

Its values are more tightly clustered around the mean
Its values cover a wider spread
It contains more observations
Its mean must be incorrect

Calculating variability measures

For each list, calculate the range and population standard deviation. Show your method and round the standard deviation to 2 decimal places.

5.Auckland's afternoon temperatures over seven days were 17, 21, 20, 24, 19, 22 and 25 °C. Put the values in order, then find the range, mean and population standard deviation.

6.A small café records the number of takeaway coffees sold on seven mornings: 38, 46, 41, 53, 44, 49 and 45. Calculate the range, mean and population standard deviation. Round the standard deviation to 2 decimal places.

Interpreting and applying variability

Use statistical language to support your conclusions.

7.Over six games, Maia scored 32, 34, 33, 35, 31 and 33 points. Luca scored 40, 25, 36, 29, 42 and 26 points. Both players have a mean of 33 points. Maia's standard deviation is about 1.29 points and Luca's is about 6.68 points. Which player was more consistent? Explain what the standard deviations show.

8.A weather station compares rainfall in two months. Month A has a range of 19 mm and a standard deviation of 5.7 mm. Month B has a range of 34 mm and a standard deviation of 12.4 mm. Which month's rainfall was more predictable? Explain using both measures.

9.A data set includes a very low value and a very high value. If both extremes are removed, what will usually happen to the range? What is likely to happen to the standard deviation, and why?

10.A school is choosing between two bus routes. Both routes have the same average travel time, but one has a much larger standard deviation. Which route would be preferable for students who need to arrive at a set time? Explain your choice.