Chapter 2 & 3
1. Relative Frequency = Frequency/n
2. Median
a. Odd : (n +1)/2 th observation
b. Even: average of (n/2)th and ( (n/2) + 1)th observation
3. Percentiles: (p/100)(n+1) = Lp
4. Mean = (x1 + x2 + ….. + xn)/n
a. No matter what value we multiply by the data set, the mean, median, mode, range, and
IQR will all be multiplied by the same value.
b. If you add a constant to every value, the mean and median increase by the same
constant.
5. Range = Largest Observation - Smallest Observation
6. IQR = Q3 - Q1
7. Deviation from Mean: (observation - mean)
8. Sample Variance:
9. Sample Standard Deviation: square root of the sample variance
a. In other words, if you add or subtract the same amount from every term in the set, the
standard deviation doesn't change.
b. If you multiply or divide every term in the set by the same number, the SD will change.
SD will change by that same number. The mean will also change by the same number.
10. Coefficient of Variation:( (standard deviation/mean) * 100)%
11. Skewness Formula:
a. Right skewed: median < mean
b. Left skewed: mean < median
12. Detecting Outliers:
a. If the data point is less than Q1- 1.5(IQR) or greater than Q3 + 1.5(IQR).
b. If the data point is 3 standard deviations away from the mean.
13. Sample Covariance: Sxy =
a. A positive value indicates a positive relationship.
b. A negative value indicates a negative relationship.
14. Sample correlation coefficient = rxy = sxy/(sx * sy) = sample covariance/ std dev of x *std dev of y
a. Values near -1 indicate a strong negative linear relationship
b. Values near +1 indicate a strong negative linear relationship
c. Always between -1 and 1
d. Closer to 0, the weaker the relationship.
Chapter 4
15. Permutations (when order matters):
16. Combinations (when order does not matter):
17. Addition Rule of Probability:
18. Mutually exclusive events: P( A OR B) = P(A) + P(B) because P(A AND B) is a null set.
19. Complements: P(A) = 1 - P(NOT A)
a. Similarly, P(NOT A) = 1 - P(A)
b. Not A is denoted by A with a bar on top or A raised to the power C
20. Check slides 44, 45, 46, 47, 48, 49, 50, 54 for very important points in Chapter 4.
21. Conditional Probability Formula : P (A| M) = P (A and M)/ P (M)
22. Multiplication Rule for Dependent Events:
23. Independent Events when
a. P (A) = P (A|B) OR
b. P(B) = P( B| A)
c. Knowing one event occurred gives you no new information about another event
occuring.
24. Multiplication Rule for Independent Events:
a. Since P(A|B) = P(A) therefore,
b. P ( A and B) = P (A) * P(B)
c. If A and B are stat independent then their complements are also stat independent. Even
A and B^C as well as A^C and B are stat independent.
25. Slide 71 has important information on the difference between mutually exclusive events and
independent events. Mutually exclusive events are not independent events.
26. Bayes Theorem: Important slides are 78, 79 and 82.
Chapter 5
27. Discrete and continuous Random Variable:
28. Discrete Uniform Probability Function: f(x) = 1/n
a. Where n = no. of values random variable may assume
29. Mean of discrete random variable:
30. Variance of discrete random variable:
31. Alternative formula for Variance for discrete random variable:
32. The expected Value of a Random Variable is its mean.
33. Expected Value of Functions of Random Variables:
a. If R = g(X)
b. E(R) = E [ g (X) ] = Summation [(g (x) * p (x)]
34. Expected Value of Squared Deviations from the mean = variance ( check slide 28)
35. Rules of Expected Value and Variance on Slide 29
36. An alternative expression of Variance using Expected Value Operator ( slide 30)
37. Bernoulli Random Variables: Take on 2 values ( 0 and 1) with probabilities ( 1 - pi) and pi
respectively.
38. Characteristics of Binomial Experiment on slide 33.
39. Binomial Distribution Formula:
40. Mean of Binomial Variable = n * pi or n * success probability
41. Variance of Binomial Variable = n * pi * (1 - pi) or np (1-p)
Chapter 6
42. Probability of continuous RV assuming a particular value = 0.
43. Probability of continuous RV is considered area under the curve.
44. Uniform Probability Distribution:
45. Mean and Variance for UPD:
46. For specific values = think of probability as length and breadth of a triangle
47. Converting x into z value for normal distribution
Chapter 7
48.