AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Levels of organisation: calculate arithmetic means
To calculate an arithmetic mean, add every value in the data set and divide the total by the number of values.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 6 of 11
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
To calculate an arithmetic mean, add every value in the data set and divide the total by the number of values. The method is the same whether the data are masses in g, lengths in mm, counts of organisms or temperatures in °C, and the mean carries the same unit as the original measurements. For example, five quadrat counts of 4, 7, 6, 8, 5 give a total of 30 and a mean of 30 ÷ 5 = 6 organisms per quadrat. With a frequency table, multiply each value by its frequency, add those products, then divide by the total frequency. Means are used to compare experimental groups and to smooth out random variation between repeats, but an extreme outlier can pull the mean away from the typical value.
What earns the marks
- Adds all the values in the data set correctly, including repeated values counted each time.
- Divides the total by the number of values, not by the number of distinct values.
- Calculates a mean from a frequency table by summing value × frequency and dividing by total frequency.
- Attaches the correct unit to the mean and rounds sensibly to match the precision of the data.
- Uses the mean to compare two groups or to summarise repeat measurements in a practical context.
Common mistakes and how to put them right
Dividing by the number of rows in a frequency table instead of the total frequency.
Put it right by adding the frequency column first.
Leaving the mean without a unit or copying the wrong unit.
Put it right by carrying the unit of the original measurements through the division.
Rounding too early in a multi-step calculation.
Put it right by keeping full values until the final answer.
Treating an outlier as an error and deleting it without justification.
Put it right by reporting it and considering the median as well.
Exam tips
- Lay out the addition as a single sum before dividing, so an arithmetic slip is easy to spot and method marks are clear.
- For frequency tables, write the value × frequency products in a working column before adding them.
- Give the mean to a sensible number of decimal places or significant figures and always include the unit.
Try the lesson
The start of the Levels of organisation: calculate arithmetic means lesson, made from checked teaching notes for this specification point.
Have a go first
A student counts the number of stomata in five equal areas of a leaf and records 4, 6, 5, 5 and 5. Calculate the arithmetic mean number of stomata per area.
Listen
To calculate an arithmetic mean, add every value in the data set and divide the total by the number of values. The method is the same whether the data are masses in g, lengths in mm, counts of organisms or temperatures in °C, and the mean carries the same unit as the original measurements. For example, five quadrat counts of 4, 7, 6, 8, 5 give a total of 30 and a mean of 30 ÷ 5 = 6 organisms per quadrat. With a frequency table, multiply each value by its frequency, add those products, then divide by the total frequency. Means are used to compare experimental groups and to smooth out random variation between repeats, but an extreme outlier can pull the mean away from the typical value. A strong answer earns marks for these points. Adds all the values in the data set correctly, including repeated values counted each time. Divides the total by the number of values, not by the number of distinct values. Calculates a mean from a frequency table by summing value × frequency and dividing by total frequency. Attaches the correct unit to the mean and rounds sensibly to match the precision of the data. A common slip: Dividing by the number of rows in a frequency table instead of the total frequency. Instead, adding the frequency column first. Exam tip: Lay out the addition as a single sum before dividing, so an arithmetic slip is easy to spot and method marks are clear.
Key words
Say what each word means before you turn the card.
arithmetic mean
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outlier
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random variation
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See every definition
- arithmetic mean
- Add every value in the data set and divide the total by the number of values.
- outlier
- An extreme value that can pull the mean away from the typical value.
- random variation
- Variation between repeats that means are used to smooth out.
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