Statistics for the LCAT: lesson and practice
The mean is the total divided by the count, and the median is the middle value after sorting (the average of the two middle values when the count is even). Standard deviation measures how spread out values are. Outliers pull the mean much more than the median. For average problems, work with totals, not averages.
Loading practice…
| Measure | How to find it | Affected by outliers? |
|---|---|---|
| Mean | Total ÷ count | Strongly |
| Median | Middle value when sorted | Very little |
| Range | Max − min | Strongly |
| Standard deviation | Spread around the mean | Strongly |
Work with totals
Average 84 on 4 tests → total 336
Next score needed: 336 − 249 = 87
Common mistakes
Sample questions with answers
1. What is the median of 11, 12, 30, 26, 14, 35?
- 24
- 20 (correct)
- 21.33
- 28
Sorted: 11, 12, 14, 26, 30, 35. Middle values 14 and 26 average to 20.
2. Average 83 on 3 tests. What score on the 4th makes the average 84?
- 84
- 85
- 87 (correct)
- 88
Needed total 336 minus current 249 is 87.
3. Values 14, 17, 24, 29, 35, 105. If 105 is removed, what happens?
- Only the mean decreases
- Both decrease; the mean decreases more (correct)
- Both decrease; the median decreases more
- Neither changes
The outlier pulls the mean much more than the median.
Frequently asked questions
Do I need to calculate standard deviation?
No. LCAT questions ask you to compare spread, not compute it.
How does an outlier affect mean and median?
It moves the mean a lot and the median only a little.
Is statistics tested on the LCAT?
Yes. It falls under Problem-Solving and Data Analysis, one of the content domains LUMS lists for the LCAT in its official sample questions.
Can I practice this without a calculator?
Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.