1. BUS7010 Quant Prep Statistics in Business and Economics
Week 5
Dr. Jenne Meyer
BUS7010 Quant Prep Statistics in Business and Economics

2. Measure of Central Tendency
A single value that summarizes a set of data. It locates the center of the values
Arithmetic mean
Weighted mean
Median
Mode
Geometric mean

3. ARITHMETIC MEAN ARITHMETIC MEAN
Pop mean = sum of all the values in pop
# of values in the pop
µ = ∑X N

4. Properties of arithmetic mean
Every set of interval data has a mean
All values are included
Mean is unique - only one
Useful to compare two or more populations
Sum of the deviations of each value from the mean will always be zero
Disadvantage of arithmetic mean
Mean may not be representative
Can’t use for open-ended (range) data

5. Median
The midpoint of the values (exactly half are below, half are above)
Used when the mean is not representative due to high value outliers
Unique number
Not affected by extremely large or small values
Can be used with open-ended range values
Can be used for several measurement types

6. Mode The value that appears most frequently
Can be used fir any measurement type
Not affected by extremely large or small values
Sometimes it doesn’t exist
Sometimes it represents more than one value

7. Formulas in Excel

8. Skewness – Mean, Median, Mode

9. Measures of Dispersion
Range
Mean deviation
Variance
Standard deviation
Range = highest value – lowest value
Mean deviation – the arithmetic mean of the absolute values of the deviations from the mean
The # deviates of average x amount from the mean
Variance – the arithmetic mean of the squared deviations from the mean
Compare the dispersion of two or more sets of data
Standard deviation – the square root of the variance
represents the spread or variability of the data, the average range from the center point

10. Variation
Population variation
=varp(…)
Sample variation
=var(…)

11. Standard Deviation Population variation Sample variation =stdevp(…)

12. Sample Standard Deviation
Sample standard deviation is most common use of statistics

13. Standard Deviation Example: Numbers Mean Standard Deviation
100,100,100,100,100,
90, 90, 100, 110,
Computing the standard deviation:
find the mean (100)
find the deviation/variance of each value form the mean (-10, -10, 0, 10, 10)
square the deviations/variances (100, 100, 0, 100, 100)
sum the squared deviations ( = 400)
divide the sum by the # of values minus 1 (# of values = 5 – 1 = 4, /4 = 100)
take the square root of the variance (10)
(Will be important in research when you are trying to determine the range of information.)

14. Coefficient of Variation
To compare dispersion in data sets with dissimilar units of measurement (e.g., kilograms and ounces) or dissimilar means (e.g., home prices in two different cities) we define the coefficient of variation (CV), which is a unit-free measure of dispersion:

15. Formulas in Excel

16. Time Series Analysis

17. Frequency curves
Normal distribution

18. Central Limit Theorem Chebyshev’s Theorem
If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution. This approximation improves with larger samples. (the larger the sample, the more it appears to be a normal standard distribution)

19. Central Limit Theorem Chebyshev’s Theorem

20. Central Limit Theorem Chebyshev’s Theorem

21. Standard Normal Distribution
Z value – converts the actual distribution to a standard distribution. (It is the distance between the selected value (x) and the mean (µ) divided by the standard deviation (σ)
Normal distributions can be transformed to standard normal distributions by the formula:
A “Z” score always reflects the number of standard deviations above or below the mean a particular score is
A person scored 60 on a test with a μ=50 and σ=10, then he scored 1 standard deviations above the mean. Converting the test score to a Z score, an X of 70 would be:
Z=1=0.3413
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22. Standard Normal Distribution
Standard Normal Table (once z is computed)
A table of probabilities for a Z random variable.
See page 479
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23. Example p 224/5, likelihood of finding a foreman w/ a salary between $1000 and $1100 is 34.13%

25. Standard Normal Distribution
p227
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