Find a missing value using the mean
Imagine you're planning a group trip and need to figure out how much everyone has spent so far. If one person forgets their total, you can use the mean average to estimate their missing amount! By knowing the average and the other totals, you can calculate the missing value to keep everything fair. This skill is handy in real life for budgeting, data analysis, and even science experiments! Jump to the questions
Practise now
Follow the steps to find the missing value.
Topic guide
What this worksheet practises
This worksheet focuses on working backwards from a given mean to find a missing data value. This is a common problem-solving scenario where you know the "target" average (like a required exam grade) and need to calculate what the final piece of data must be to hit that target.
Key method
The secret to these problems is calculating the total sum of the numbers.
- Multiply the given mean by the total number of items (including the missing one) to find the total sum required.
- Add up all the numbers you currently have.
- Subtract your current total from the required total sum.
- The difference is your missing value.
Worked example
A student has taken 4 tests and scored 60, 75, 80, and 65. What must they score in their 5th test to achieve a mean average of 70?
Step 1: Calculate the total sum required for 5 tests.
Total = Mean × Number of tests = 70 × 5 = 350.
Step 2: Add up the scores they already have.
Current total = 60 + 75 + 80 + 65 = 280.
Step 3: Subtract the current total from the required total.
Missing score = 350 − 280 = 70.
They must score 70 in their final test.
Common mistakes to avoid
The most common mistake is trying to find the mean of the existing numbers (in our example, finding the mean of the 4 tests) and then somehow manipulating that number to get the target mean. This is overly complicated and prone to error. Always focus on calculating the total sums instead.
How to check your answer
Once you have found your missing number, perform a standard mean calculation using all the numbers to verify. (60 + 75 + 80 + 65 + 70) ÷ 5 = 350 ÷ 5 = 70. The result matches the target mean, confirming your answer is correct.