For the data 3, 1, 7, 5, 9, what are the mean and median?
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Answer
Mean 5, median 5
Sum 25 over 5 values gives 5. Sorted: 1, 3, 5, 7, 9, so the middle value is 5. The raw middle entry (7) is not the median until you sort.
Statistics Workout
Probability, distributions, inference and regression, with worked answers
Statistics Workout is a Bertopia flashcard pack of 61 cards: probability, distributions, inference and regression, with worked answers. It covers describing data; probability; counting; distributions; sampling; confidence intervals and tests; correlation and regression.
Sample cards
You flip 4 fair coins. What is the probability of exactly 2 heads?
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Answer
3/8
C(4, 2) = 6 of the 16 equally likely outcomes, so 6/16 = 3/8.
How many ways can you choose 3 people from 10 for a committee?
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Answer
120
Order does not matter: C(10, 3) = 10 × 9 × 8/3! = 120. 720 counts ordered picks.
A fair coin is flipped 5 times. What is P(exactly 2 heads)?
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Answer
0.3125
C(5, 2)(0.5)⁵ = 10/32 = 0.3125.
What does the central limit theorem say?
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Answer
Sample means are roughly normal for large n
The CLT is about the distribution of the sample mean. The population itself keeps its shape.
A sample of 100 has mean 50, and σ = 15 is known. What is the 95% confidence interval for the mean?
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Answer
50 ± 2.94
Margin = 1.96 × 15/√100 = 1.96 × 1.5 = 2.94.
Sources
2 sources
- OpenStax, Introductory Statistics 2e, OpenStax, Rice University
- NIST/SEMATECH e-Handbook of Statistical Methods, NIST
