1. Quantitative Techniques – Class I
Making Data Simple

2. What is Statistics?
Study of the collection, organization, analysis, interpretation and presentation of data
Theoretical statistics – the mathematical basis of the process of statistical analysis. Most research and work on finding new tools, fixing errors in existing tools and improving them
Applied Statistics – using the existing tools of statistics on certain data to improve our understanding of the problem in hand
What type of assumptions?
What is Normal?
Simple concept like average (mean) and standard deviation

3. Concepts Population and Sample Mean Median Standard Deviation
Risk Adjusted Returns
Basic Probability
Sample Selection
Measurement Bias
Spreadsheets and Relational Data
Charting your Data – Pie Charts, Bar Graphs, Histograms

4. Types of Data Nominal Data – Groups
Ordinal Data – Has some meaningful order
Interval Data – Ordinal data, but same intervals
Ratio Data
Data can be continuous or discrete

5. Descriptive Statistics
Mean
Median
Mode
Percentile
Interquartile Range
Standard Deviation

6. Charts Bar Charts – Perfect for Discrete Data with Only few categories
Stacked Charts – When Comparing Similar Bars, over time
Pie Chart – When the proportions are important, not the actual values
Box Plot – Median, shown with the Interquartile Range, and Extended Line showing the Minimum and Maximum Values (Range)
Histograms – Display continuous data, similar to par charts, but can be used for more categories, since it shows a trend
Scatterplots – Show the relation between two variables
Line Graphs

7. Probability - Definitions
Sample Space – Like population, the entire range of values possible
Event – The actual realization of the values
Union – The likelihood of either of multiple events occurring
Intersection – The likelihood of both events occurring
Complement – Everything in the sample that is not occuring
Mutual Exclusivity – If one event occurs, then the other cannot
Independence – When the events are not related to each other – that is, the probability of one, does not affect the other
Permutations – The number of ways to arrange some objects
Combinations – Permutation, when order is not important

8. Rules (Axioms) of Probability
An “event” E will occur or not occur
P(E) is a number that equals the probability that E will occur.
By convention, 0 < P(E) < 1.
E' = the event that E does not occur
P(E') = the probability that E does not occur.

9. Essential Results for Probability
If P(E) = 0, then E cannot (will not) occur
If P(E) = 1, then E must (will) occur
E and E' are exhaustive – either E or E' will occur.
Something will occur, P(E) + P(E') = 1
Only one thing can occur. If E occurs, then E' will not occur – E and E' are exclusive.

10. Joint Events Pairs (or groups) of events: A and B
One or the other occurs: A or B ≡ A  B
Both events occur A and B ≡ A  B
Independent events: Occurrence of A does not affect the probability of B
An addition rule: P(A  B) = P(A)+P(B)-P(A  B)
The product rule for independent events:
P(A  B) = P(A)P(B)

11. Independent Events
Events are independent if the occurrence of one does not affect probabilities related to the other.
Events A and B are independent if P(A|B) = P(A). I.e., conditioning on B does not affect the probability of A.

12. Expected Value Toss a coin If you get head, you make Rs. 10
If you get tail, you make Rs. 2
What is your expected value?
Remember, probability of Head = 0.5 (50%)
Probability of Tail = 0.5 (50%)
EV = 0.5 x x 2 = Rs. 6
If someone says that you can take this bet for Rs. 5 then you should always take it