Formula sheet
Mean (ungrouped)
x̄ = Σx / N is printed on the SPM formula sheet, so it is given in the exam, you do not memorise it. What you must know is when to apply it (for a list of ungrouped values), how to add every value correctly into Σx, and how to count N.
What the symbols mean
- x̄ the mean (average), in the same unit as the data
- Σx the sum of all the data values
- x each individual data value
- N the number of data values
Given in the exam, or memorise?
x̄ = Σx / N is printed on the SPM formula sheet, so it is given in the exam, you do not memorise it. What you must know is when to apply it (for a list of ungrouped values), how to add every value correctly into Σx, and how to count N.
Why it works
The mean shares the total equally among all the values, the single number every value would become if the total were spread evenly.
- Add every value together to get the grand total Σx.
- Count how many values there are; call it N.
- Divide the total by the count: sharing Σx among N values gives the balancing point x̄.
Worked example 1
Five students scored 62, 75, 80, 68 and 90 marks in a test. Find the mean mark.
- List the 5 marks: 62, 75, 80, 68, 90.
- Add them: Σx = 62 + 75 + 80 + 68 + 90 = 375.
- Count the values: N = 5.
- Apply the formula: x̄ = Σx / N = 375 / 5.
Worked example 2
A shop records the number of customers on 6 days: 24, 30, 28, 34, 22 and 30. Find the mean number of customers per day.
- List the daily counts: 24, 30, 28, 34, 22, 30.
- Add them: Σx = 24 + 30 + 28 + 34 + 22 + 30 = 168.
- Count the days: N = 6.
- Apply the formula: x̄ = Σx / N = 168 / 6.
Where students go wrong
- Dividing by the wrong N, miscounting the values or forgetting that a repeated value (e.g. 30 twice) is still counted each time.
- A slip when adding Σx on the calculator; always re-check the total before dividing.
- Confusing the mean with the median or mode, the mean is total ÷ count, not the middle or the most common value.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I need to memorise the mean formula for SPM?
No. x̄ = Σx / N is printed on the exam formula sheet, so it is given.
What you must know is when to use it, how to add every value into Σx, how to count N exactly, and how to divide. Marks come from correct working and the right unit, not from recall.
What is the difference between mean and average?
In SPM the mean is the arithmetic average: the total of all values divided by how many values there are. When a question simply says 'average', it almost always means this mean.
Median and mode are different measures, so read the command word carefully before deciding which one to find.
Does the mean have to be a whole number?
No. The mean is often a decimal even when every data value is a whole number, because you are dividing the total by N.
Leave it as an exact fraction or round as the question asks, usually to two decimal places, and always write the correct unit.