Misunderstood Concepts

Question 1

What is the formula for the location (L) of a yth percentile in an array with n entries sorted in ascending order?

Answer 1

The formula for the location (Ly) of a yth percentile in an array with n entries sorted in ascending order is Ly = (n + 1) × (y/100). In this case, n = 10 and y = 80%, so

L80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.

the 8.8th position would be between the eighth and ninth entries, 20.65 percent and 27.37 percent, respectively. Using linear interpolation, P80 = X8 + (Ly − 8) × (X9 − X8),P80 = 20.65 + (8.8 − 8) × (27.37 − 20.65)
= 20.65 + (0.8 × 6.72) = 20.65 + 5.38
= 26.03 percent.

Question 2

The fourth quintile is equivalent to the ___ percentile.

Answer 2

80th

Question 3

What does “Percentile” refer to?

Answer 3

A percentile is a statistical measure indicating the value below which a given percentage of observations in a group of observations falls. Essentially, percentiles help to understand the relative standing of a value within a data set.

Question 4

What is “Target Semideviation”?

Answer 4

Definition: Target semideviation calculates the standard deviation of all returns that fall below a chosen target or benchmark. It is a measure of downside risk, highlighting how returns deviate from the minimum acceptable return (MAR).

Question 5

How do you calculate “Target Semideviation”?

Answer 5

The target semideviation is the square root
of the sum of the squared deviations from the target,
divided by n-1.

Question 6

What is the coefficient of variation?

Answer 6

The coefficient of variation (CV) is a statistical measure of the relative dispersion or variability of a data set in relation to its mean. It is often expressed as a percentage and provides a standardized measure of the spread of the data points, allowing for comparison between distributions of scores that may have different units or different means.

Question 7

What is a “unimodal dataset”?

Answer 7

A unimodal distribution in statistics refers to a frequency distribution that has only one peak. Unimodality means that a single value in the distribution occurs more frequently than any other value. The peak represents the most common value, also known as the mode.

Question 8

What does “Skewness” refer to?

Answer 8

The location of the dataset’s tail end.

Question 9

If a graph is “Positively Skewed” is the graphs tail on the “left” or “right”?

Answer 9

right.

Question 10

What is the relationship between “Mean, Median, and Mode” of a negatively-skewed graph?

Answer 10

Mean < Median < Mode

Question 11

What is the relationship between “Mean, Median, and Mode” of a positively-skewed graph?

Answer 11

Mean > Median > Mode

Question 12

What is kurtosis and why is it useful?

Answer 12

Kurtosis is a statistical measure that describes the shape of a distribution’s tails in relation to a normal distribution. It provides insight into the likelihood of extreme outliers in the data set and the overall peakiness or flatness of the distribution.

Question 13

What does “Lepto” mean?

What is “Leptokurtosis”?

Answer 13

lepto means narrow

“kleptos” have a “narrow” insterest in fire.

Leptokurtosis represents “narrow” graphs.

Question 14

What does “Meso” mean?

What is “Mesokurtosis”?

Answer 14

meso means middle

mesokurtosis represents “medium” graphs (in terms of kurtosis)
(i.e., a more “normal” distribution)

Question 15

What does “Platy” mean?

What is “Platykurtosis”?

Answer 15

Platy means “plate” or “flat”

Platykurtosis represents “flat” graphs (in terms of kurtosis)

Question 16

How do you calculate “Variance” from mean and probability?

Answer 16

Variance =
Sum of All:
(Mean - Observation)^2 * Probability(Observation)

Question 17

How do you calculated “Standard Deviation” from “Variance”?

Answer 17

Std dev = sqrt(variance)

Question 18

What is Bayes’ theorem?

Answer 18

P(A |B ) = P(B | A) * P(A) / P(B)

Question 19

How do you find the “unconditional probability of an event given new information”?

Answer 19