Range & Outliers
What is the range?
- The range is the difference between the highest value and the lowest value
- range = highest - lowest
- For example, the range of 1, 2, 5, 8 is 8 - 1 = 7
- range = highest - lowest
- The range is a simple measure of how spread out the data is
- The range does not measure an average value
- Ranges of different data sets can be compared to see which is more spread out
- Be careful with negatives
- The range of -2, -1, 0, 4 is 4 - (-2) = 6
How do I find the range from a table?
- When data is presented in a frequency table, or as grouped data, you still need to find the maximum and minimum data values
- Look out for any frequencies of zero; there are no data values in these rows!
- Be careful with the limits of grouped data
- If the lowest data value is in the group labelled 3 < x ≤ 6, use 3 as the lowest data value
- If the highest data value is in the group labelled 18 < x ≤ 22, use 22 as the highest data value
- This means the range will be an estimate in this case, as we do not know the actual data values in each class interval
- e.g. The lowest data value could actually be 4
What is an outlier?
- An outlier is a data point which is abnormally different to the rest of the data
- e.g. A group of students' heights in cm could be 170, 165, 175, 168, 162, 199
- The 199 cm measurement would likely be regarded as an outlier
- e.g. A group of students' heights in cm could be 170, 165, 175, 168, 162, 199
- The range should not be used if there are any outliers
- For example, the range of 1, 2, 5, 80 is 80 - 1 = 79
- This is not a good measure of spread
- The range is easily affected by extreme values
- For example, the range of 1, 2, 5, 80 is 80 - 1 = 79
Exam Tip
- If asked to find the range in an exam, make sure you show your subtraction clearly (don't just write down the answer)
Worked example
Find the range of the following data.
| 3.4 | 4.2 | 2.8 | 3.6 | 9.2 | 3.1 | 2.9 | 3.4 | 3.2 |
| 3.5 | 3.7 | 3.6 | 3.2 | 3.1 | 2.9 | 4.1 | 3.6 | 3.8 |
| 3.4 | 3.2 | 4.0 | 3.7 | 3.6 | 2.8 | 3.9 | 3.1 | 3.0 |
Range = highest value - lowest value
9.2 - 2.8
The range is 6.4
Worked example
Find the largest possible value for the range of the following data.
| Weight, w kg | Frequency |
| 3 ≤ w < 3.5 | 0 |
| 3.5 ≤ w < 4 | 4 |
| 4 ≤ w < 4.5 | 6 |
| 4.5 ≤ w < 5 | 5 |
| 5 ≤ w < 6 | 0 |
To find the range, find the minimum and maximum data values, and find the difference
The top row does not contain any data, so the minimum value will be the smallest possible value in the 3.5 ≤ w < 4 class interval
Lowest value = 3.5 kg
The bottom row also does not contain any data, so the maximum value will be the largest possible value in the 4.5 ≤ w < 5 class interval
Highest value = 5 kg
Find the range
Range = 5 - 3.5 = 1.5
1.5 kg
This will only be an estimate for the range, as we do not know exactly which values are in each class interval
