Module 7.2: Means and Variance Flashcards
What are the properties of an arithmetic mean?
1) All interval and ratio data sets have an arithmetic mean
2) All data values are considered and included in the arithmetic mean computation
3) A data set has only one arithmetic mean (i.e the arithmetic mean is unique)
4) The sum of the deviations of each observation in the data set from the mean is always zero.
When is the median a better measure of central tendency than the mean?
If the mean has outliers that are either really large or small compared to the rest of the population
When can a geometric mean be used?
when calculating investment returns over multiple periods or when measuring compound growth rates.
What is the geometric mean formula?
[[[(1+R1)(1+R2)(1+R3)] ^ (1/3)] - 1]
On TI enter rate[yx]3[1/x]
What is a harmonic mean?
What is the formula?
Used for certain computations such as average cost of shares purchased over time.
Formula: N / (1/P1) + (1/P2)
N = time period
P = price or other variable
For values that are not equal, what is the typical ranking of means from lowest to highest
Harmonic Mean < Geometric Mean < Arithmetic Mean
What is a quartile?
What is the formula for data points sorted in ascending order?
General term for a value at or below which stated proportion of the data in a distribution lies.
Ly = (n +1) y /100 y = given percentile n = data points
What is the third quartile for the following distribution of returns?
8%, 10%, 12%, 13%, 15%, 17%, 17%, 18%, 19%, 23%
Ly = (n +1) y /100
Ly = (10+1) * 75/100 = 8.25
then you count 8 to the right, 18% add on .25.
75% of all observations are below 18.25%
What is the range of a data set?
The difference between the maximum value and the minimum value
What is the mean absolute deviation? How is it calculated using below return %?
[30%, 12%, 25%, 20%, 23%]
Average of absolute values of the deviations of individual observations from the arithmetic mean.
1) calculate the arithmetic mean = 22%
2) Take each return % and subtract the arithmetic mean
3) take absolute value of each number, add all 5 together and divide by 5.
What is population variance? Population standard deviation? What is the population variance using the below numbers?
[30%, 12%, 25%, 20%, 23%]
Population variance is defined as the average of the squared deviations from the mean.
1) calculate the arithmetic mean = 22%
2) Take each return % and subtract the arithmetic mean and then square it.
3) take absolute value of each number, add all 5 together and divide by 5.
What is greater the MAD or standard deviation of a sample?
Standard deviation > MAD holds generally.
Why do we use the sample size - 1 for the sample size variance as opposed to the sample size?
Using the sample size will systematically underestimate the population parameter, particularly for small sample sizes.
What is the formula for sample variance?
The same as population variance except the denominator is n -1, rather than n.
