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Statistics and Probability Formulas
1 / 20
What is the formula for the variance of a data set?
Variance σ² = Σ(x-μ)²/n. It is the average of the squared deviations from the mean.
2 / 20
What is the formula for the weighted average?
Weighted average = Σ(value × weight) / Σ(weights). Used in GPA calculation, grade weighting, etc.
3 / 20
What does a box plot (box-and-whisker plot) display?
A box plot shows the 5-number summary: minimum, Q1 (25th percentile), median (Q2), Q3 (75th percentile), and maximum.
4 / 20
What is residual in a regression?
Residual = observed y - predicted y. A residual plot helps assess if a linear model is appropriate.
5 / 20
What is an outlier in a data set?
An outlier is a data point significantly different from the rest. It can heavily affect the mean but not the median.
6 / 20
What is the formula for the number of outcomes in the sample space of rolling two dice?
Two dice: 6 × 6 = 36 total outcomes. Use the multiplication principle for independent events.
7 / 20
How do you calculate the mean?
Mean = Sum of all values ÷ Count. It is the arithmetic average of a data set.
8 / 20
What does it mean when two events are independent?
Independent events: P(A|B) = P(A). The occurrence of B does not change the probability of A.
9 / 20
What is Bayes' Theorem formula?
Bayes' Theorem: P(A|B) = P(B|A)×P(A)/P(B). It updates probability based on new evidence.
10 / 20
What is the formula for permutations (nPr)?
Permutations: nPr = n! / (n-r)!. Order DOES matter in permutations.
11 / 20
How do you find the number of ways to arrange n distinct items?
The number of arrangements of n distinct items = n! (n factorial). Example: 4 items = 4! = 24 ways.
12 / 20
In a normal distribution, what percentage of data falls within 1 standard deviation of the mean?
68-95-99.7 rule: ~68% falls within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD of the mean.
13 / 20
How is standard deviation related to variance?
Standard deviation = √variance. Taking the square root brings the measure back to the original units.
14 / 20
What is the expected value formula?
Expected value: E(X) = Σ(x × P(x)). Multiply each outcome by its probability and sum them all.
15 / 20
What does a z-score of 2 mean?
A z-score of 2 means the value is 2 standard deviations above the mean.
16 / 20
What is a histogram?
A histogram displays the frequency distribution of continuous data using adjacent bars. The x-axis shows intervals; y-axis shows frequency.
17 / 20
What does P(A|B) represent?
P(A|B) is conditional probability: the probability of A occurring given that B has already occurred.
18 / 20
What is the formula for the coefficient of variation?
Coefficient of Variation CV = (σ/μ) × 100%. It expresses standard deviation as a percentage of the mean, allowing comparison across different scales.
19 / 20
What does a correlation coefficient of r = 1 indicate?
r = 1 indicates a perfect positive linear relationship. r = -1 is perfect negative; r = 0 is no linear correlation.
20 / 20
What is the formula for the probability of at least one event occurring?
P(at least one) = 1 - P(none occur). It's easier to find the complement (probability of nothing happening).
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