Measures of Location and Dispersion

Question 1

Quantile (fractile) is…

Answer 1

a value at or below which a stated fraction of the data is situated.

Question 2

Interquartile range (IQR) is…and is calculated as…

Answer 2

the difference between the third and first quartiles of a dataset.

IQR = Q3 − Q1

Question 3

Formula for finding the percentile is…

Answer 3

L y (percentile) = (n + 1)(y/100)

Question 4

What is dispersion?

Answer 4

The variability of a population or central around the central tendency.

Question 5

What is absolute dispersion?

Answer 5

The amount of variability present without comparison to any reference point or benchmark.

Question 6

Measures of absolute dispersion include:

Answer 6

1)Range
2)Mean Absolute Deviation (MAD)
3)Variance
4)Standard Deviation

Question 7

The range is?

Answer 7

A difference between the minimum and maximum values within the dataset.

Question 8

The mean absolute deviation (MAD) for a sample formula is:

Answer 8

MAD = Summation of (Deviations Xi - Xbar) / n

Question 9

Sample variance can be defined as?

Answer 9

The expected value (the probability-weighted average) of squared deviations from a random variable’s expected value.

Question 10

The Sample Variance formula is:

Answer 10

S2 = Summation of (variable - sample mean)^2 / n - 1

Question 11

Standard Deviation can be defined as?

Answer 11

The positive square root of the variance: a measure of dispersion in the same units as the original data.

Question 12

Standard Deviation can be fined by?

Answer 12

S = Squared root of Sample Variance

Question 13

Sample standard deviation can help us to understand…?

Answer 13

The gap between the arithmetic mean and the geometric mean.

Question 14

The relation between the arithmetic mean (Xbar) and geometric mean (Xbar sub-G) is calculated as:

Answer 14

Xbar (sub-G) ≈ Xbar - s^2 / 2

Question 15

Downside risk is defined as?

Answer 15

Risk of incurring return below a specified value.

Question 16

Target Semidiviation - a measure of..,.?

Answer 16

Downside risk.

Question 17

Target Semidiviation (Starget) formula is…?

Answer 17

S target semi.d. = √Σ(Xi - B)^2 / n-1

Where Xi is the sum of all deviations,
B is the target,
n is the total number of sample observations.

Question 18

Relative Dispersion is the amount of…?

Answer 18

Dispersion relative to a reference value or benchmark.

Question 19

Coefficient of Variation Formula is useful when comparing means from…and different…?

And is calculated as?

Answer 19

Comparing means across different data sets or when different units of measurements.

CV = s/Xbar