A frequency table packs repeated scores into rows, so each row can represent several students. Count scores to find the median’s middle position, and use the greatest frequency to find the mode. For the mean, use paired score-frequency columns in Desmos so every score counts as often as it occurs. Count students, not table rows.
Hints
- Hint 1
The median is the middle score after every student’s score is put in order. With an odd number of students, one position sits in the middle. Which position is it, and which score fills it?
- Hint 2
The mode is the score that appears most often, not the highest score or the frequency number. Find the greatest frequency, then read the score paired with it.
- Hint 3
The mean uses every student’s score. A row with frequency contributes three copies of its score. In Desmos, pair each score with its frequency so the calculation includes all the students.
Step-by-step
Count positions, then calculate the mean
Step 1Find the middle position
With 15 students, the median is the middle score after all scores are ordered. That’s position : seven scores come before it and seven come after it.
- Step 2
Locate the eighth score
The s fill positions through , and the s fill positions through . The four s fill positions through , so the eighth score is . The median is . Don’t pick a middle table row; a row can hold several scores.
- Step 3
Find the most frequent score
The mode is the score that occurs most often. The greatest frequency is , paired with , so the mode is . The counts students; it isn’t their score.
- Step 4
Calculate the mean with frequencies
The mean is the total of all 15 scores divided by . In Desmos, enter each score in beside its frequency in . Then type to multiply each score by its frequency before dividing by the number of students. Desmos shows , or with the fraction button.
- Step 5
Compare the three measures
The mode and median tie at , below the mean of about . So the quiz scores have . Choice C.