AI Statistics Solver
Statistics summarises data with a few meaningful numbers. This AI statistics solver computes the mean, median, spread and probabilities and shows each calculation, so you can reproduce it in an exam.
Measures of centre and spread
- Mean: add all values and divide by how many there are.
- Median: the middle value after sorting; for an even count, the average of the two middle values.
- Mode: the most frequent value.
- Range: largest minus smallest.
- Variance and standard deviation: how far values typically sit from the mean.
Population versus sample
When your data is the whole group, divide the sum of squared deviations by n (population). When it is a sample from a larger group, divide by n − 1 (sample), which corrects for bias. Always check which version your course expects; the solver shows both when it is unclear.
Basic probability
Probability is favourable outcomes divided by total outcomes when all outcomes are equally likely. For combinations, use C(n, r) = n! / (r!(n − r)!). Enter data as a list, for example Find the mean and standard deviation of 4, 8, 6, 5, 7. For graphing or counting questions presented as stories, the word problem solver can help set them up.
Worked examples
Example 1: Find the mean, median and standard deviation of 4, 8, 6, 5, 7
- Mean: (4 + 8 + 6 + 5 + 7) ÷ 5 = 30 ÷ 5 = 6.
- Sorted: 4, 5, 6, 7, 8, so the median is 6.
- Deviations from 6: −2, 2, 0, −1, 1; squares: 4, 4, 0, 1, 1; sum = 10.
- Population variance = 10 ÷ 5 = 2, so SD = √2 ≈ 1.414. Sample variance = 10 ÷ 4 = 2.5, so SD ≈ 1.581.
Final answer: Mean 6; median 6; population SD ≈ 1.414; sample SD ≈ 1.581
Example 2: Find the median of 3, 7, 8, 12
- There are four values, so average the middle two.
- (7 + 8) ÷ 2 = 7.5.
Final answer: 7.5
Example 3: Two fair dice are rolled. What is the probability the total is 7?
- There are 6 × 6 = 36 equally likely outcomes.
- Totals of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), which is 6 outcomes.
- 6/36 simplifies to 1/6.
Final answer: 1/6
Example 4: In how many ways can you choose 2 students from 5?
- Use C(5, 2) = 5! / (2! × 3!).
- = (5 × 4) ÷ 2 = 10.
Final answer: 10
Common mistakes to avoid
- Forgetting to sort the data before finding the median.
- Using n instead of n − 1 for a sample.
- Taking the square root too early when calculating standard deviation.
- Treating a mean as the “typical” value when outliers distort it.
- Counting ordered pairs when the question asks for combinations.
Frequently asked questions
What is the difference between mean and median?
The mean uses every value and is pulled by extremes; the median is the middle value and is more robust to outliers.
When do I use n − 1?
When the data is a sample used to estimate a larger population’s variance or standard deviation.
Can the solver handle frequency tables?
Yes. Type the values with their frequencies in AI mode and it will compute weighted statistics.
Does it cover normal distribution problems?
Basic z-score and probability questions are supported through AI mode. Check tables if your course requires them.
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AI-generated solutions are for learning purposes. Always verify important answers.