Find the range of 14, 9, 21, 6 and 18.
Averages and Range - Edexcel GCSE Higher Maths
Typically 3-6 marks per paper · Spec 1MA1
Mean, median, mode and range are spec ref S4 on Edexcel 1MA1, and they are crossover content: the same question can appear near the end of a Foundation paper and near the start of a Higher one. At Higher tier you are rarely asked for a plain average from a short list. The marks sit in the variations, above all in working backwards from a mean to a missing value and in reading averages out of a frequency table.
Edexcel writes two recognisable question types here. The first gives you data and asks for a calculation, usually with a frequency table so that the mean needs a sum of divided by the total frequency rather than a sum of rows divided by the number of rows. The second gives you two sets of data and asks you to compare them, which is a written answer worth 2 marks: one comparison of a measure of average and one of spread, both quoting numbers and both mentioning what the data is about.
The comparison mark is the one most often lost, and it is lost for the same reason each time. An answer saying one group did better says nothing a mark scheme can credit. An answer saying the median for class B is 4 marks higher, and its range is 3 marks smaller so its results are more consistent, has both halves and both numbers. Practise writing that sentence pattern until it is automatic, then check every calculation with the sanity test that a mean must lie between the smallest and largest values.
Worked example
Ten students take a test. Their mean mark is 62.
An eleventh student takes the same test and scores 84.
Work out the mean mark of all eleven students.
[3 marks]- Turn the mean back into a total. Ten students with a mean of 62 scored marks between them.M1: mean multiplied by the frequency to recover the sum, the step the whole question turns on
- Add the new mark to that total: .M1: new total formed from their sum plus 84
- Divide by the new number of students: .A1: 64, dividing by 11 rather than by 10
Practice questions
These are original questions in Edexcel 1MA1 Higher style. Expect frequency tables, missing values and combined groups rather than short lists, since that is how the topic is set at Higher tier. Papers 2 and 3 allow a calculator, but every question here is small enough to do by hand as practice for Paper 1.
No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.
Question 1 Warm-up [1 mark] Question 2 Warm-up [1 mark] Find the mode of 5, 7, 7, 9, 11, 7 and 5.Question 3 Exam pace [3 marks] A football team scored these numbers of goals in 25 matches. 0 goals: 6 matches 1 goal: 8 matches 2 goals: 7 matches 3 goals: 3 matches 4 goals: 1 match Work out the mean number of goals per match.Question 4 Exam pace [3 marks] Two numbers have a mean of 17 and a range of 6. Find the larger number and the smaller number.Question 5 Exam pace [1 mark] A frequency table has a total frequency of 60. Which value is the median?Question 6 Stretch [3 marks] 14 students recorded a score. Score 10: 3 students Score 11: 4 students Score 12: 5 students Score 13: 2 students Find the median score.
Common mistakes examiners see
Finding the mean of a frequency table by adding the values and dividing by how many rows there are, so a table with values 1 to 5 always gives a mean of 3.
Add an column, total it, and divide by the total frequency, not by the number of rows. A quick check: if 40 people answered, the divisor is 40.
Reading the median off an unsorted list, or taking the middle row of a frequency table as the median.
Sort the list first, then use the position. In a frequency table, run a cumulative total down the column until you pass that position, and the value on that row is the median.
Giving the range as the two extreme values, writing 'from 12 to 31' instead of 19.
The range is one number, the largest minus the smallest. If the answer has two numbers in it or a unit like 'to', it is not a range.
Comparing two data sets by describing only the averages, or by saying one set is 'better' with no figures.
Write two sentences, one about an average and one about spread, each with a number and each phrased about the context: 'the median time is 5 seconds lower' and 'the range is 8 seconds smaller, so the times are more consistent'.
In a missing-value question, guessing a value that looks reasonable instead of using the total the mean implies.
Multiply the mean by the number of values to get the total that must be reached, subtract the values you already have, and what is left is the missing one. It is one calculation, and it is where the method mark is.
Frequently asked questions
- Which average should I use?
- The median when the data has an extreme value, because one very large or very small figure drags the mean with it. The mode when the data is categorical, such as favourite colour, since you cannot add colours. The mean otherwise, because it uses every value. If a question asks you to justify the choice, say what the extreme value does to the mean.
- How do you find the mean from a frequency table?
- Multiply each value by its frequency to make an column, add that column, and divide by the total frequency. For a grouped table you use the midpoint of each class in place of the value, which is why the answer is an estimate.
- Is the range a measure of average?
- No. The range measures spread, which is how far apart the values are, while mean, median and mode measure the average. Edexcel comparison questions ask for one of each, so quoting two averages and no spread scores half the marks.
- How many marks are averages worth on Edexcel Higher?
- Usually 3-6 marks across a paper. A frequency table mean is typically 3 marks, a missing value question 3, and a comparison of two distributions 2. The topic also appears inside cumulative frequency, box plot and histogram questions, where the averages are read off a graph instead.