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Statistics Flashcards

1
Q

Measurement Scales

A

“N” Nominal
“O” Ordinal
“I” Interval
“R” Ratio

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2
Q

Population Mean Formula

A
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3
Q

Sample Mean Formula

A
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4
Q

Weighted Mean Formula

A
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5
Q

Geometric Mean Formula

A

Used when calculating investment returns over multiple periods (TWM) or when measuring compound growth rates.

Harmonic < Geometric < Arithmetic

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6
Q

Geometric Mean Return Formula

A
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7
Q

Harmonic Mean Formula

A

Used to compute average cost of shares purchased over time.

Harmonic < Geometric < Arithmetic

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8
Q

Position of a percentile in an array with n entries

A
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9
Q

Mean Absolute Deviation Formula (MAD)

A
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10
Q

Population Variance Formula

A
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11
Q

Population Standard Deviation Formula

A
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12
Q

Sample Variance Formula

A
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13
Q

Sample Standard Deviation Formula

A
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14
Q

Coefficient of Variation Formula

A

Measures risk (variability) per unit of expected return (mean). Higher CV is riskier.

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15
Q

Sharpe Ratio Formula

A 
R(p) = portfolio return
R(f) = risk-free return
S(p) = standard deviation of portfolio returns
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16
Q

Chebyshev’s Inequality

A

For any distribution with finite variance, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1-1/k^2 for all k>1

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17
Q

Dispersion

A

Measures the variability around the central tendency (mean). Addresses risk.

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18
Q

Skewness

A

the extent to which a distribution is not symmetrical.

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19
Q

Left Skewed Distribution

A
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20
Q

Right Skewed Distribution

A
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21
Q

Kurtosis

A

Statistical measure that tells us when a distribution is more or less peaked than a normal distribution. Kurtosis = 3 for normal distributions.

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22
Q

Leptokurtic distribution

Lung Measured Pulmonary Function Test

Leptokurtic More Peaked Fatter Tail

A

A distribution that is more peaked than a normal distribution. Kurtosis > 3 (excess kurtosis > 0)

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23
Q

Platykurtic distribution

A

A distribution that is less peaked than a normal distribution. Kurtosis < 3 (excess kurtosis < 0)

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24
Q

Mesokurtic

A

A distribution identical to the normal distribution.

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25
Descriptive v. Inferential statistics
descriptive- summarizes important characteristics of large data sets while inferential- pertain to procedures used to make forecasts, estimates, and judgements on the basis of a smaller set (sample)
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population
set of all possible members of a stated group; example- cross-section of the returns of all of stocks traded on the NYSE
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sample
subset of the population of interest
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nominal scales
nominal scales-least accurate level of measurement; counted or classified with no order; example assigning number 1 to a municipal bond fund, the number 2 to a corp bond fun, and so on
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ordinal scales
every observation is assigned to one of several categories, which are then ordered with respect to a specified characteristic; -example -the ranking of 1,000 small cap growth stocks by performance may be done by assigning the number 1 to the 100 best performing stocks, the number 2 to the next 100 best performing stocks, and so on
30
interval scale
provide relative ranking, like ordinal, but differences between scale values are equal (like temperature); WEAKNESS: 30 degrees F is not 3x as hot as 10 degrees F (called zero point as the origin) like ratio scales
31
Ratio scales
provide ranking and equal diff b/t scale values and have a true zero point as the origin so $4 is 2x as much as $2; think NOIR - nominal, ordinal, interval, ratio
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parameter
characteristic of a population such as the mean return or the SD of returns
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sample statistic
used to measure a characteristic of a sample
34
frequency distribution
summarizes statistical data by assigning it to specified groups, or intervals
35
intervals
aka classes
36
sample statistic
used to measure a characteristic of a sample
37
frequency distribution
summarizes statistical data by assigning it to specified groups, or intervals
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how to construct a frequency distribution
1. Define the intervals to which data measurements (observations) will be assigned. Make sure all are mutually exclusive. 2. Tally the observations 3. Count them and find the interval with the greatest frequency called the modal interval Example- annual returns on a stock
39
modal interval
interval with the greatest absolute frequency
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relative frequency
percentage of total observations falling within each interval
41
cumulative absolute frequency or cumulative relative frequency
all the frequencies added up in order; relative means percentage-wise
42
histogram
graphical representation of the absolute frequency distribution; bar chart of continuous data classified into a frequency distribution
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frequency polygon
shape of the histogram with just a line like a line graph; however, the line intersects the midpoints
44
measures of central tendency
identify the center, or average, of a data set, which can be used to represent the typical, or expected, value in the data set
45
population mean
mean of all observed values in the population; it's unique so that means there's only one mean
46
sample mean
mean of all the values in a sample of a population; used to make inferences about the population
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unimodal, bimodal, trimodal
unimodal- means there's one value that appears most frequently; bimodal- two values that appear most frequently
48
harmonic mean
average cost of shares over a certain period of time
49
mean absolute deviation MAD
average of the absolute values of the deviations of individual observations from the arithmetic mean; calculating SD, basically
50
biased estimator
mean of all observed values in the population; it's unique so that means there's only one mean
51
Chebyshev's inequality
minimum percentage of any distribution that will lie within a certain SD of the mean; 1-(1/k)^2
52
Limitations of the Sharpe ratio
if 2 portfolios have negative sharpe ratios, the higher one isn't necessarily superior because increasing risk moves a negative Sharpe ratio closer to zero 2. if asymmetic return distributions, not normal
53
kurtosis
measure of how much a distribution is more or less peaked than a normal distribution
54
Leptokurtic v. platykurtic v. mesokurtic
lepto-more peaked or sharper! v. platy - less peaked or flatter! and meso- the same!!
55
how are kutosis and skewness useful and why?
they are critical in a risk management setting because when securities returns are modeled using an assumed normal distribution, the predictions from the models will not take into account for the potential for extremely large, negative outcomes;
56
which is generally riskier? higher or lower skewness? kurtosis?
in general, greater positive kurtosis and more negative skew in returns distributions indicates increased risk
57
Sample skewness
58
when is skewness signficant?
when S k is in excess of 0.5
59
how to find excess kurtosis?
excess kurtosis = sample kurtosis - 3
60
sample kurtosis
measured using deviations raised to the fourth power
61
Coffecient of Variation
62
Population Variance
The population variance is equal to the sum of the squared differences between each population member and the population mean divided by the number of items in the population Alternatively It is equal to the average squared observations less the squared mean .
63
Mean Deviation
The mean deviation is the absolute values of the deviation from the mean and then taking there average
64
Characteristics of Skewness
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Charateristics of Mean
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Skewness
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SKewness
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Relationship between Sharpe Ratio and Risk
Higher the Sharpe Ratio higher the risk
89
Relative Dispersion
Coefficient of Variation Rishab Dev Ka CV is high
90
Survey questionnarire where choices has to be selected
Mode and Median are the best options
91
Normal Distribution and Standard Deviation
92
Which measures of central tendencies are not affected by extreme high or low values ?
Mode and Median
93
Normal Distribution and Standard Deviation
94
Relationship between Airthmetic Mean and Geometric Mean
The airthmetic mean and the geometric mean are equal when volatility in the rate of return is zero. For a non zero volatility the mean exceeds the geometric mean and as the difference is larger higher the volatility
95
What is the disadvantage of the range
It only takes into account 2 values
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