Download Quantitative Techniques * Class I

Quantitative Techniques –
Class I
Making Data Simple
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
Concepts
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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
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
Descriptive Statistics
• Mean
• Median
• Mode
• Percentile
• Interquartile Range
• Standard Deviation
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
Probability - Definitions
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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
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.
Essential Results for Probability
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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.
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)
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.
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 10 + 0.5 x 2 = Rs. 6
• If someone says that you can take this bet for Rs. 5 then you should
always take it