Statistical Concepts and Market Returns

Question 1

Statistics that summarize the characteristics of a data set

Answer 1

Descriptive statistics

Question 2

Statistics that are used to make probabilistic statements about a population based on a sample

Answer 2

Inferential statistics

Question 3

Data is put into categories that have no particular order

Answer 3

Nominal scale

Question 4

Data is put into categories that can be ordered with respect to some characteristic

Answer 4

Ordinal scale

Question 5

Differences in data values are meaningful, but ratios, such as twice as much or twice as large, are not meaningful

Answer 5

Interval scale

Question 6

Ratios of values are meaningful, and zero represents the complete absence of the characteristic being measured

Answer 6

Ratio scale

Question 7

Any measurable characteristic of a population

Answer 7

Parameter

Question 8

A characteristic of a sample

Answer 8

Sample statistic

Question 9

The percentage of total observations falling within an interval

Answer 9

Relative frequency

Question 10

The sum of the relative frequencies for all values less than or equal to that interval’s maximum value

Answer 10

Cumulative relative frequency

Question 11

Arithmetic Mean

Answer 11

Mean = Sum of all values / n

Question 12

Geometric Mean (compound growth rate)

Answer 12

Mean = (1+X1 x 1+X2….)^1/n

Question 13

Harmonic Mean

Answer 13

Mean = N / (1/x1) + (1/x2)…

Question 14

Mean Absolute Deviation

Answer 14

MAD = Σ (|X1 - Mean| + |X2 - Mean|) / n

*Absolute values

Question 15

The mean of the squared deviations from the arithmetic mean or from the expected value of a distribution

Answer 15

Variance

Question 16

Population Variance

Answer 16

= Σ (Xi - μ)^2 / N

Question 17

Sample Variance

Answer 17

= Σ (Xi - x-bar)^2 / n - 1

Question 18

Chebyshev’s inequality

Answer 18

= 1 - (1/k^2)

The proportion of the observations with k standard deviations of the mean

Question 19

Coefficient of Variation

Answer 19

= s / x-bar

Question 20

The degree to which a distribution is not symmetric about its mean

Answer 20

Skewness, > .5 = significantly different from 0

Question 21

The measure of peakedness of a distribution and the probability of extreme outcomes

Answer 21

Kurtosis, normal is = 3, excess kurtosis > 1 = significant

Question 22

Leptokurtic

Answer 22

Positive excess kurtosis (fat tails, more peaked) = probability of extreme outcomes is greater than a normal distribution

Question 23

Platykurtic

Answer 23

Negative values of kurtosis (thin tails, less peaked)

Question 24

When is the arithmetic mean appropriate? When is the geometric return appropriate?

Answer 24

Mean = forecasting single period returns in future periods

Geometric = forecasting future compound returns over multiple periods