Thoughts on Business and Technology

Statistics & Probability

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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