Mean / median swap sprint

Report the mean when the median is asked, or vice versa.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid mixing up the mean and the median

The mean and the median are both called an "average", and the trap answer is usually the other one.

The two values are far apart here because 15 is an outlier. An outlier pulls the mean toward it, but it moves the median very little. Test writers put both values in the choices.

Check habits:

Worked examples

Example 1.
A student recorded these 7 quiz scores: 30, 42, 24, 14, 29, 15, 35. What is the mean (average) score?
Show answer and explanation
Answer:
D

Mean = sum \(\div\) count = 189 \(\div\) 7 = 27. (Reporting the median (the middle of 14, 15, 24, 29, 30, 35, 42) gives 29. Dividing by 6 instead of 7 (\(189 \div 6\)) gives 31.5. Averaging only the largest and smallest scores (\((42 + 14) \div 2\)) gives 28.) The mean score is 27.

Example 2.
The stem-and-leaf plot shows 12 test scores (stem = tens digit, leaf = ones digit). What is the median score?
STEM-AND-LEAF PLOT
StemLeaves
12 4
25 7 8
32 4 5
43 3 3 9
Show answer and explanation
Answer:
A

Reading off the leaves gives the sorted scores: 12, 14, 25, 27, 28, 32, 34, 35, 43, 43, 43, 49. With 12 scores, the median is the average of the two middle scores: (32 + 34) \(\div\) 2 = 33. (Reporting the mean (\(385 \div 12\)) gives about 32.08. Adding the two middle scores but not dividing by 2 (\(32 + 34\)) gives 66. Using only the lower of the two middle scores gives 32.) The median score is 33.

Example 3.
A delivery truck drives 27 miles in 1.5 hours, then 133 miles in 150 minutes. What is the delivery truck's average speed for the entire trip, in miles per hour?
Show answer and explanation
Answer:
C

Average speed \(=\) total distance \(\div\) total time, NOT the average of the leg speeds. Total distance \(= 27 + 133 = 160\) mi. Total time \(= 1.5 + 150 \div 60 = 4\) h. Average speed \(= 160 \div 4 = 40\) mph. (Averaging the two leg speeds gives 35.6 mph. Writing 150 minutes as 1.5 hours (\(160 \div (1.5 + 1.5)\)) gives about 53.3 mph. Using the first leg's speed only (\(27 \div 1.5\)) gives 18 mph.)