Compute and interpret measures of central tendency, and recognize how outliers pull the mean away from the median — the three measures rarely agree, and knowing which one a question actually wants matters as much as calculating it correctly. Every question comes with a written walkthrough of exactly how each measure was found.
The median is the middle value of the sorted list — finding the middle of an unsorted list gives a value with no particular meaning.
For an even number of data points, the median is the average of the two middle values after sorting, not either one of them alone.
With a strong outlier in the data set, the median describes the "typical" value far better than the mean does — picking the mean automatically, without checking for outliers, misrepresents the data.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Find the mean of the data set: 12, 15, 18, 9, 40
A — 18.8. Add all five values: 12+15+18+9+40 = 94, then divide by the count, 5: 94/5 = 18.8. 15 (B) is the median of this data set — the middle value once sorted — not the mean, a common mix-up between the two measures since they usually land close together but don't have to.
The mean of five numbers is 20. Four of the numbers are 14, 22, 18, and 25. Find the fifth number.
A — 21. The mean formula gives the total sum: mean × count = 20 × 5 = 100. The four known values sum to 14+22+18+25 = 79, so the fifth number is 100−79 = 21. 5 (D) comes from mixing up the count of numbers (5) with an actual data value, rather than solving the sum equation.
A data set of 6 test scores has a mean of 82. Five of the scores are 78, 85, 90, 95, and 85. Find the sixth score, then state whether the data set has a mode.
A — 59; mode is 85. The mean gives the total: 82×6=492. The five known scores sum to 78+85+90+95+85=433, so the sixth score is 492−433=59. Checking the mode: 85 appears twice in the full set of six scores, more than any other value, so the mode is 85. 65 (C) comes from an arithmetic slip adding the five known scores. 59; no mode (B) gets the sixth score right but misses that 85 repeats in the data set.
Mean, median, and mode problems are quick once the definitions are locked in — most of the difficulty comes from choosing which measure a question actually wants, not from the arithmetic itself.
Always write the data set in sorted order first, even for a straightforward-looking problem. Untimed practice is where that habit becomes automatic.
Move to timed sessions once sorting and each formula are instant. These should be some of the fastest Statistics questions once the habit sticks.
Pair mean, median, and mode with basic probability in a mock — both subtopics reward careful reading of what a data set or sample space actually contains.
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