HSPT: Averages: find a missing value
Learn to find a missing value from a mean by working with totals, and to find the score needed to reach a new average.
If you know the average and all but one value, how do you find the missing value?
Short answer
Multiply the mean by the number of values to get the total. Then subtract the values you know.
Know first: Finding a mean, Multiplying and adding whole numbers
Step 1 of 5
A mean is a total shared equally
The mean, or average, is the total of the values divided by how many values there are. Turn that around and you get the key fact for missing-value questions: total = mean × count.
If you know the mean and the count, you know what all the values must add to. Subtract the values you have, and what is left is the missing one.
Step 2 of 5
Use the total to find the missing score
Worked example: A missing test score
Four test scores have a mean of 85. Three of them are 80, 92 and 78. What is the fourth score?
- A90
- B85
- C340
- D5
- 1
Find the total
4 × 85 = 340.
- 2
Add the known scores
80 + 92 + 78 = 250.
- 3
Subtract
340 − 250 = 90.
- 4
Check
(250 + 90) ÷ 4 = 340 ÷ 4 = 85.
- 5
See why the other choices are there
85 is the mean, not the missing score. 340 is the total of all four. 5 multiplies the mean by 3, the number of known scores, instead of by 4.
Answer
90
Wrong: Total = 85 × 3 = 255, so the missing score is 255 − 250 = 5.
Right: Total = 85 × 4 = 340, so the missing score is 340 − 250 = 90.
Multiply the mean by the number of values in the whole set, including the missing one. Using only the known values leaves one score out.
Step 3 of 5
Find the total first
Check yourself · Question 1
Six numbers have a mean of 7. Five of them are 4, 9, 6, 11 and 3. What is the sixth number?
Answer: B
The total must be 6 × 7 = 42. The five known numbers add to 33. The sixth is 42 − 33 = 9.
Trap answer: 7
Repeating the mean
- Why it looks right
- The mean is a value that "belongs" to the set, so it feels like a natural fill-in.
- Why it's wrong
- The known numbers add to 33, which is below 5 × 7 = 35. So the missing number has to be above 7 to bring the mean up.
- The right answer
- 9, because 33 + 9 = 42 and 42 ÷ 6 = 7.
Check yourself · Question 2
Maria's mean score on 4 quizzes is 82. What score on her fifth quiz would raise her mean to 85?
Answer: B
Her current total is 4 × 82 = 328. For a mean of 85 over 5 quizzes, she needs 5 × 85 = 425. The fifth score must be 425 − 328 = 97.
Common mistake
"To raise my average by 3, I just need a score 3 points higher."
- Why it's tempting
- It feels like the new score only has to beat the target by the amount of the change.
- Do this instead
- One score has to raise the mean of every quiz. Work with totals: the new total minus the old total is the score needed.
Step 4 of 5
What to remember
Remember
- Total = mean × number of values.
- The missing value is the total minus the values you know.
- Use the count of the whole set, including the missing value, and check by dividing.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
What total did the scores need in the practice question, and which wrong choice is the mean itself?