Mean, Median, Mode and Range
Section: Statistics | Syllabus: Cambridge Primary Mathematics (0845)
Mean, Median, Mode and Range
- The mode, median, mean and range are all ways to describe and summarise a set of data
- The mode, median and mean are often called averages - they each describe a typical or central value
- The range describes how spread out the data is, not an average
Finding the Mode
- The mode is the value that occurs most often in a data set
- A data set can have more than one mode - this is called bimodal
- A data set can have no mode at all if every value occurs the same number of times
Finding the Median
- The median is the middle value once the data is arranged in order of size
- Always write the data in order, from smallest to largest, before finding the middle
- If there are two middle values, the median is halfway between them - add the two values together and divide by 2
Finding the Mean
- The mean is found by adding together all the values and dividing by how many values there are
- Mean = total of all values ÷ number of values
Finding the Range
- The range shows how spread out a data set is
- Range = highest value - lowest value
| Statistic | What it tells you | How to find it |
|---|---|---|
| Mode | The most common value | Find the value that appears most often |
| Median | The middle value | Order the data, then find the middle |
| Mean | The "share out equally" average | Total ÷ number of values |
| Range | How spread out the data is | Highest − lowest |
Worked Example: Finding All Four Statistics
Question: A football team scored this many goals in 7 matches:
2, 5, 3, 5, 1, 5, 3
Find the mode, median, mean and range of this data.
- Mode:
- 5 appears three times - more often than any other value
- Mode = 5
- Median:
- Order the data first: 1, 2, 3, 3, 5, 5, 5
- There are 7 values, so the middle (4th) value is the median
- Median = 3
- Mean:
- Total = 2 + 5 + 3 + 5 + 1 + 5 + 3 = 24
- Mean = 24 ÷ 7 = 3.43 (2 d.p.)
- Range:
- Highest value = 5, lowest value = 1
- Range = 5 − 1 = 4
The tallest bar shows the mode - the value that occurred most often
Worked Example: A Bimodal Data Set
Question: Find the mode of this data set: 4, 7, 4, 9, 7, 2
Answer: Both 4 and 7 appear twice, more often than any other value, so this data set has two modes: 4 and 7. This is called bimodal data.
Common Mistakes
MistakePicking the middle value of the data before putting it in order
Fixalways order the data from smallest to largest first - "the middle value" only makes sense once the data is in order
MistakeForgetting to divide by 2 when there are two middle values
Fixwith an even number of values, add the two middle numbers together and divide by 2 to find the median
MistakeDividing the total by the number of different values instead of the total number of values when finding the mean
Fixdivide by how many numbers are in the data set altogether, including any that repeat
MistakeAssuming every data set has exactly one mode
Fixa data set can be bimodal (two modes) or have no mode at all if no value repeats more than any other
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