Question 41·Medium·One-Variable Data Distributions; Measures of Center and Spread
The scores on five quizzes are , and .
The mean of the five scores is .
What is the median of the five scores?
When a mean is given with one unknown data point, immediately translate it into an equation: set the mean equal to (sum of all values) divided by the number of values, then solve for the unknown. After you know all data points, sort them if needed and, for an odd number of values, pick the exact middle one as the median—do not confuse the median with the mean or with the largest value.
Hints
Relate the mean to the total sum
If the mean of 5 quiz scores is 85, what must the total of the 5 scores be? Write an equation using .
Solve for the unknown score
Once you know the total sum of all 5 scores, subtract the sum of the four known scores (, and ) to find .
Use the definition of the median
After you find , write all five scores in increasing order. For 5 numbers, which position in the ordered list gives you the median?
Desmos Guide
Use Desmos to solve for the unknown score
Type the expression (72+85+88+90+x)/5 into Desmos. Adjust the slider for x until the value of the expression is 85; the value of x at that point is the missing quiz score .
List all five scores and find the middle one
Using the value of you found, list the five scores (72, 85, 88, 90, and ) in increasing order. Identify the middle (3rd) number in this ordered list; that value is the median.
Step-by-step Explanation
Use the mean to find the unknown score
The mean of 5 numbers is their sum divided by 5. Set up the equation using the given mean of 85:
Multiply both sides by 5:
So
Add the known scores:
Then
So the five scores are , and .
Order the scores and find the median
To find the median, list the scores in increasing order (they already are):
With 5 numbers, the median is the middle (3rd) number in the ordered list. The 3rd number is 88, so the median is 88.