Practice · Grade 8 statistics
Mean, Median & Mode — Practice
Work through the three averages from easy to hard, then beat one boss question on the median of an unsorted list. Hints and full solutions, free.
Q1 of 7
0 correct
Find the mean of these three numbers.
(3 + 5 + 7) ÷ 3
Quick answer
What is the best way to practice mean, median and mode?
Practice the three averages separately. Mean: add all the numbers and divide by how many there are. Median: sort the list by size first, then read off the middle value — with an even count, average the two middle ones. Mode: count which value occurs most often. Work five or six problems of increasing difficulty, and pay special attention to always sorting before you take the median — that is where most mistakes happen.
HowTo
A 4-step solving strategy
This order works for any mean, median or mode problem.
- 1Step 1 of 4
Read: which average is asked for?
Mean, median or mode? Each is calculated differently. Mark the measure being asked in the problem before you start computing.
- 2Step 2 of 4
Mean: sum divided by count
Add all the values and divide by how many there are. Example: (4 + 8 + 15 + 16 + 23 + 42) ÷ 6 = 18.
- 3Step 3 of 4
Median: sort first, then the middle
Sort the values by size. With an odd count the median is the middle value; with an even count it is the average of the two middle values.
- 4Step 4 of 4
Count the mode — and sanity-check
Count which value occurs most often. Finally ask yourself: does the mean fall between the smallest and largest value? If not, there is a calculation error.
Examples
Worked examples with full solutions
Four typical problem types. Try each yourself first, then compare with the solution.
Easy
Mean of 4, 8, 15, 16, 23, 42
Sum = 4 + 8 + 15 + 16 + 23 + 42 = 108
108 ÷ 6
= 18
Check: 18 lies between 4 and 42 ✓
A classic mean: sum divided by count.
Medium
Median of 4, 8, 15, 16, 23, 42
ordered: 4, 8, 15, 16, 23, 42
two middle values: 15 and 16
(15 + 16) ÷ 2 = 15.5
Check: equally many values left and right of 15.5 ✓
Even count — the median is the average of the two middle values.
Easy
Mode of 2, 4, 4, 5, 7, 4, 9
4 appears 3×
every other value only 1×
mode = 4
Check: no number is more frequent than the 4 ✓
The mode is the most frequent value, not the average.
Hard
Median of 12, 4, 7, 4, 1, 8 (unsorted)
sort: 1, 4, 4, 7, 8, 12
two middle values: 4 and 7
(4 + 7) ÷ 2 = 5.5
Check: three values left, three right of 5.5 ✓
Forget to sort and you read off the wrong middle — here that would be fatal.
Pitfalls
Common mistakes — and how to avoid them
These five traps keep coming up with averages.
Not sorting before the median
The median is the middle value of the sorted list. Unsorted, you read off the wrong number — always sort first.
Taking only one value with an even count
With 6 values there are two middle ones. The median is their average, not either one alone.
Confusing the mode with the mean
The mode is the most frequent value, the mean is the average. The two can be far apart.
Miscounting the count for the mean
Divide by the count of all values, not by a guessed number. Count the values carefully.
Not checking the result for plausibility
The mean and median must lie between the smallest and largest value. If something falls outside, there is a calculation error.
Study
Practice with a plan — three short tips
Identify the average first, then compute
For every problem, ask first: mean, median or mode? The method afterwards is routine — choosing the right one is the real lesson.
For the median: make sorting a habit
Rewrite every list in sorted order before taking the median. Build that habit and you will never make the most common mistake again.
For every wrong answer: why?
Was it a counting slip? Forgotten sorting? The wrong average? Note the cause — next time you will spot the mistake right away.
FAQ
Frequently asked questions about practising
Glossary
Terms in one sentence
- Arithmetic mean
- The sum of all values divided by how many there are — the "average".
- Median
- The middle value of the list sorted by size.
- Mode
- The value that occurs most often in a data series.
- Measure of central tendency
- A single figure that summarises a data series with one typical value.
- Outlier
- A single value that differs sharply from the rest.
- Bimodal
- A data series with two equally frequent values that occur most often.
- Boss question
- The last and hardest problem of a practice set, combining several steps.