#### Statistics & Probability

— May 8, 2013# Statistics

**Descriptive Statistics** – sample set is 100% of population

**Inferential Statistics** – sample is subset of population with a % chance or probability of being wrong in its inference

**Stochastic -** Randomly determined; having a random probability distribution or pattern that may be analyzed statistically but may not be predicted.

## Frequency Distribution

This breaks up data into groups or classes and shows the number of observations in each class.

**Absolute Frequency Distribution -** count the number of observations in each group/class

**Relative Frequency Distribution -** is obtained by obtained by dividing the number of observations in each class/group by the total number of observations in the data as a whole. ( total being 1.0 , each group ranges from 0 to 0.9 ) [ useful when you want to categorize your observations into groups based on ranges, ex- number of calls with response times btw 0-10 ms, 10-20 ms etc ]

**Cumulative Frequency Distribution -** each progressing group is a sum of observations of the previous group ( assuming ascending order ) including the observations in the current group [ useful when you want to identify total number of observations below each threshold, ex- number of calls with response times below 10, 20, 30, 40 etc ]

** Central Tendency -** Mean, Median , Mode

**Dispersion -** Average deviation, Variance , Standard deviation

# Probability

Probability : Desired outcome / All possible/likely outcomes

**Ways to Find Probability : **

Logical – If we know all likely events ( and lack any historical data )

Relative Frequency – When we have historical data ( when the number of experiments tend to infinity Relative = Logical )

Subjective – When we dont have any data, usually based on experience/Gut feeling/knowledge of Environment ( useful for personal probability – )

Probability is more useful when you have a large sample set and you can diversify your bets across multiple events.

**Rules of Probability : **

1. Probability of Independent events : P(a) * P(b) [ Probability of defect A and defect B in a single process ]

2. Probability of Dependent events / Conditional Probability -

3. Probability of Mutually exclusive events : P(a) + P(b) [ combined probability of defects in process A and process B, where Process A and B are exclusive ]

4. Probability of Non-Mutually exclusive events : P(a) + P(b) – P(a & B) [ teenagers in LA with cap , watch or cap and watch ]

**Counting Possible Outcomes :**

1. Permutations : n! [ ex – 4! = 4*3*2*1 ]

2. Combinations : n! / r! (n-r)!

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