A missing quiz score and a given mean tell you to find the total first. Write the mean equation, then use a Desmos regression to find the missing score. Put all five scores in order before finding the median, or middle score. The mean fixes the total, but it doesn't tell you which score is in the middle.
Hints
- Hint 1
The mean is the sum of the scores divided by the number of scores. Include all five scores, even though one is called . What equation says their mean is ?
- Hint 2
A Desmos regression finds the unknown value that makes two sides match. Replace with in your mean equation, then read the value of under PARAMETERS.
- Hint 3
The median of five scores is the third score after sorting from least to greatest. Once you've found , put it alongside the four known scores before choosing the middle.
Step-by-step
Find the missing score, then the middle
Step 1Turn the mean into an equation
The mean is the sum of the scores divided by the number of scores. There are five scores, including , so the given mean gives you:
- Step 2
Find the missing score in Desmos
Change to and type . A regression finds the value that makes the sides match. Under PARAMETERS, Desmos shows . That's the missing score, not necessarily the median.
- Step 3
Order all five scores
Put alongside the four given scores. From least to greatest, they are . Keep both s: one was given, and the other is . Type to store that ordered list in Desmos.
- Step 4
Read the middle score
Type ; Desmos displays . The median is the middle score in order, so with five scores, it's the third one. The median quiz score is , not the given mean of . Choice C.