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In mathematics, the range of data is defined as the *difference* between the lowest number (minimum) and the highest number (maximum) in the data set and is useful when applied to the data obtained from repeating an experiment. The smaller the range of the repeats, the higher the precision of the experiment and the more reliable the data. Top grade candidates in science will be using mathematics to analyze their results. They could use the range to help their arguments for or against the reliability of their experiment.

Take for example these two sets of data obtained by different groups of students carrying out the same experiment:

Team A: 12, 12, 10.5, 10, 12, 10, 12.5

Team B: 14, 11.5, 12, 9, 12, 10.5, 10

Each team of students carried out the experiment 7 times and by pure chance, both sets of results give the same mean value. The range of the data of team A is 2 (their maximum value is 12.5 and their minimum 10.5) but the range for team B is 5 (their maximum value is 14 and their minimum 9) so you can say that the results of team A are more precise. If the two teams were to carry out the same experiment once more, team A would be more likely to be closer to the mean value.

1.

Which is the lower limit of this range of data?

22, 14, 16, 19, 11, 28

22, 14, 16, 19, 11, 28

11

15

16

17

The lower limit is the smallest number

2.

If the range is large, the variation of the data is...

large

small

insignificant

unchanged

The upper and lower limits are significantly different to each other and looking at possible reasons for a large spread of results could help you to suggest modifications to the experiment to increase reliability

3.

The range will guide us about a valid comparison between our experimental results and the control. If the ranges do not overlap, we say that there is...

no difference

a significant difference

a fluke

a chance that they may be different

If there is no overlap between the ranges, the experimental group must be different from the control and therefore we have a clear cut difference

4.

What is the upper limit of the following data?

15, 18, 25, 18, 45

15, 18, 25, 18, 45

15

18

25

45

The upper limit is the highest number

5.

To calculate the range, we...

subtract the largest number from the smallest

subtract the smallest number from the largest

subtract the mean from the largest number

take an average

This is a way of expressing the range as a single figure

6.

If the range is large, we need to consider this.

Repeating the experiment many more times

Leaving it and working out the average

Changing the experiment altogether

Asking for more time

If the range is very wide, it could just be the method or it could be genuine biological variation. Repeating the experiment is the best way forward as a first step to double checking the data

7.

Calculate the range of the following data.

12, 14, 16, 13, 17, 19

12, 14, 16, 13, 17, 19

Six

Seven

Eight

Nine

The upper limit is 19, the lower limit is 12 so the range is 19 - 12 = 7

8.

The range is the same thing as this.

Average

Spread

Accuracy

Median

The range gives us a measure of the spread of the data

9.

Which one of the following is the range of this data?

25, 16, 18, 10, 12, 16, 17

25, 16, 18, 10, 12, 16, 17

12 to 16

10 to 17

10 to 25

25 to 17

Remember, the range is the lowest to highest or vice-versa

10.

If there is a very wide range of data for the same experiment, we say that the data is...

precise

unreliable

ranging

inaccurate

Range is taken as a measure of reliability when applied to the repeat results of an experiment