Question 47·Medium·One-Variable Data Distributions; Measures of Center and Spread
The mean of eight test scores is 75. When the highest score is removed, the mean of the remaining seven scores decreases to 72.
What is the value of the highest score?
(Express the answer as an integer)
For mean problems where one value is added or removed, quickly convert each mean into a total sum by multiplying mean × number of values. Then relate the totals with a simple equation: original total = new total + removed value (or − added value). Solving this one-step equation is usually faster and less error-prone than trying to reason directly with averages.
Hints
Use the definition of mean
Mean (average) = (sum of all values) ÷ (number of values). How can you use this to find the total of the 8 scores and the total of the 7 scores?
Compare the two totals
Once you find the total of all 8 scores and the total of the 7 remaining scores, think about how those two totals are related by the one score that was removed.
Set up an equation for the removed score
Let the highest score be . Write an equation that shows: (sum of 7 scores) + = (sum of 8 scores). Then solve for .
Desmos Guide
Compute the total of all 8 scores
In Desmos, type 8*75 and note the result; this is the total of all 8 scores.
Compute the total of the remaining 7 scores
On a new line, type 7*72 and note the result; this is the total of the 7 scores after removing the highest one.
Find the removed (highest) score
On another line, type 8*75 - 7*72. The value Desmos shows for this expression is the highest score that was removed.
Step-by-step Explanation
Turn each mean into a total sum
The mean (average) is total sum divided by number of values.
- For the 8 test scores with mean 75, the total sum is
- For the remaining 7 scores with mean 72, the total sum is
Relate the two totals using the highest score
The total of all 8 scores equals the total of the 7 remaining scores plus the highest score.
Let be the highest score. Then:
Solve for the highest score
Solve the equation :
So, the highest test score is .