Mean, Median, and Range
These three summaries show up constantly. Mean is the average, median is the middle, range is the spread from lowest to highest.
Reading the concept isn't enough. The score comes from practicing the real Bluebook-style format and finding the exact mistakes you keep making.
What the SAT tests here
Mean: add the values, divide by how many. Median: sort, then take the middle (average the two middle values if the count is even). Range: highest minus lowest.
How to solve one, step by step
Example: data $\{4, 8, 6, 10, 2\}$.
- Mean: $\frac{4+8+6+10+2}{5} = 6$.
- Sorted $\{2,4,6,8,10\}$: median $6$; range $10 - 2 = 8$.
The mistakes that cost points
- Forgetting to sort before finding the median. The median is the middle of the ordered data.
- Mishandling an even count. With an even number of values, average the two middle ones.
Practice questions
Try these the way you would on test day, then open the solution to check your method.
Easy
The table shows the number of pets owned by households in a neighborhood. What is the median number of pets per household?
- A1
- B3
- C2
- D2.5
Show solution
Answer: C, 2. Total households = 2+5+4+3+1 = 15. The median is the 8th value when listed in order. Cumulative: 0 pets → positions 1-2; 1 pet → positions 3-7; 2 pets → positions 8-11. The 8th value is 2, so the median is 2.
Medium
The table shows the scores of two classes on the same test. Which of the following correctly compares the medians?
- AThe median of Class B is greater than Class A
- BThe median of Class A is greater than the median of Class B.
- CThe median cannot be determined from a frequency table
- DThe medians of both classes are equal
Show solution
Answer: B, The median of Class A is greater than the median of Class B.. Class A has $10$ values. Median $= $ avg of 5th and 6th values: $\frac{76 + 80}{2} = 78$. Class B median $= $ avg of 5th and 6th: $\frac{72 + 76}{2} = 74$. Class A median is greater.
Hard
A dataset has 8 values in order: 3, 5, 8, 10, 12, 15, 18, 22. A student says the median is 10 because it is the 4th value. What is the actual median?
- A$12$
- B$19$
- C$10$
- D$11$
Show solution
Answer: D, $11$. With 8 values (even count), the median is the average of the 4th and 5th values: $\frac{10 + 12}{2} = \frac{22}{2} = 11$. The student incorrectly used just the 4th value rather than averaging the middle two.
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