# ECON 2613 Study Guide - Final Guide: Billy Bishop, Reverse Engineering, Neurology

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Empirical Analysis ECON 2613

HISTOGRAMS

Steps to make a Histogram:

1) sort data into ascending order (smallest to biggest)

2)find the range of the data

3) choose how many bins you want in your histogram

4)divide the range by the number of bins this gives you the width of your bins

5)set the limits of the bins and use the COUNTIF function to find results

6)divide the COUNTIF results by the total number of observations and multiply by 100 to get frequency %

7) highlight %s and the bin lits, then put into graph

****NOTE: COUNTIF results should add up to the number of observations****

CENTRAL TENDENCY

how the data values group around a typical or central value

Masures:

>Arithmetic Mean(average) add all values/# of values

>Median n+1/2 gives position of median

>Mode most common value

>Geometric Mean {(1+R)* (1+R2) …}^1/n

VARIATION

dispersion or scattering of values

Measures:

>Range --- Largest to Smallest

>Interquartile range --- Q3-Q1 (eliminates

problems with range)

>variance(average of squared deviations from the mean) --- S^2=(value*-mean)^2/n-1

>Standard Deviation(variation about the mean)--- s=SQRT[(value-mean)^2/n-1]

>Coefficient of Variation (shows variation to mean, can compare two

or more sets of data with diff. units) --- (stdev/mean)*100

*All values in the observations not just 1 specific value. Add the differences then divide

QUARTILE MEASURES

splits the ranked data into 4 segments (each take 25% of the whole)

Q1=25% observations are smaller and 75% are greater (n+1)/4

Q2= 50% also the median (n+1)/2

Q3=75% observations are smaller and 25% are greater 3(n+1)/4

***NOTE: gives position of the value not the actual value***

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Z-Score/Z-stat

(value-mean)/stdev

Shape of a Distribution

Mean<Median=left skewed

Mean=Median = symmetric

Mean>Medain=right skewed

EMPIRICAL RULE

approx. the variation in a bell shape distribution

states that:

68% of data is within 1 stdev

95% of data is within 2 stdev

99.7% of data is within 3 stdev

Sample Covariance: ***Shows independence*****

measures strangth of the linear relationship between 2 numerical variables

SC=(xvalue-xmean)(yalue-ymean)/n-1

>0 move in same direction

<0 move in opposite directions

if =0 X and Y are independent

Correlation Coefficient

measures the relative strength of the linear relationship between 2 variables

closer to -1 negative relationship

closer to 1 positive relationship

closer to 0 weak any relationship

BINOMIAL DISTRIBUTION

Syntax: BINOMDIST(success, trials, Psuccess, total)

sucesses=#of trials which turn out positive

trials=# of trials

Psuccess= probability any given trial is a success

Total= false/true

When to use: when looking for a probability of success in a set amount of trials

ie: lottery tickets

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Empirical Analysis ECON 2613

EX: A lottery ticket pays out some winnings 22% of the time. If I buy 5, with what probability do I lose on all five?

successes = 0 trials = 5 P(success) = 0.22 total? = false

P(lose all five) = BINOMDIST(0, 5, 0.22, false) = 28.9%

A lottery ticket pays out some winnings 22% of the time. If I buy 5, with what probability do I win on two or more?

successes ≥ 2 trials = 5 P(success) = 0.22 total? = true

P(win two or more) = 1 − BINOMDIST(1, 5, 0.22,true) = 30.4%

POISSON DISTRIBUTION

Syntax=POISSON(events,average, total)

events=#of times event occurs

average=# of events we expect

total= false/true

When do we use: expected arrivals but need the probability of arrivals in a given minute or

area of opportunity. How may times it occurs in an area of opportunity.

BEWARE!!: do not confuse with Exponential

ie: production lines

EX: We are working a polling station. Based on last year’s election, we expect three arrivals per

minute. What is the probability a given minute sees nobody arrive?

events = 0 average = 3 total = false

P(events = 0) = POISSON(0, 3, false) = 4.98%

EX2: Based on JD Power quality measures, the average new Ford has 1.18 problems when it

rolls off the assembly line. What is the probability that a new Ford has at least 3 problems?

events ≥ 3 average = 1 total =

true

P(events ≥ 3) = 1−P(events < 3) = 1−POISSON(2, 1.18,true) = 11.6%

NORMAL DISTRIBUTION

Syntax: NORMDIST(point,mean,stdev,total)

point=the value you're interested in

mean=mean of the variable

stdev= standard deviation

total=false/true

When to use: when looking for a probability of hitting an exact number or outcome

ie: consuming a certain point or more/less

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