Chapter 3

Question 1

Arithmetic mean of a Sample

Answer 1

The sample mean is the sum of the values in a sample divided by the number of values in the sample symbol: x̄

Where:

x̄ = sample mean

n = number of values or sample size

x_i = ith value of the variable x

Question 2

Median

Answer 2

The middle value in an ordered array of data that has been ranked from smallest to largest. Half the values are smaller than or equal to the median, and half the values are larger than or equal to the median.

There are two rules for computing the Mean

• Rule 1 If the data set contains an odd number of values, the median is the measurement associated with the middle-ranked value
• Rule 2 If the data set contains an even number of values, the median is the measurement associated with the average of the two middle-ranked values.

Question 3

Geometric Mean

Answer 3

The geometric mean is the nth root of the product of n values:

x̄_G = (x₁*x₂*x₃…*x_n)^1/n

Question 4

Geometric Mean Rate of Return

Answer 4

The geometric mean rate of return measures the mean percentage return of an investment per time period

Ṝ_G = [(1+R₁)*(1+R₂)*…*(1+R_n)]^1/n - 1

where

R_<em>i</em> = rate of return in time period i

Question 5

Range

Answer 5

The range is equal to the largest value minus the smallest value.

Range = X_largest - X_smallest

Question 6

Sample Variance

Answer 6

S²

The sample variance is the sum of the squared differences around the mean divided by the sample size minus 1

Question 7

Sample Standard Deviation

Answer 7

S

The sample standard deviation is the square root of the sum of the squared differences around the mean divided by the sample size minus 1

Question 8

Coefficient of Variation

Answer 8

The coefficient of variation is equal to the standard deviation divided by the mean, pultiplied by 100%

Where

S = sample standard deviation

x̄ = sample mean

Question 9

Z Score

Answer 9

The Z score for a value is equal to the difference between the value and the mean, divided by the standard deviation

Question 10

First Quartile, Q₁

Answer 10

Question 11

Third Quartile, Q₃

Answer 11

Question 12

Interquartile Range

Answer 12

Question 13

The Five Number Summary

Answer 13

X_smallest Q1 Median Q3 X_largest

Question 14

Population Mean

Answer 14

The population mean is the sum of the values in the population divided by the population size, N

where

• µ = population mean
• Xi = ith value of the variable X

Question 15

Population Variance

Answer 15

The population variance is the sum of the squared differences aroudn the population mean divided by the population size, N

Question 16

Population Standard Deviation

Answer 16

The square root of the population variance

Question 17

The Empirical Rule

Answer 17

for population data from a symmetric mound-shaped distribution such as the normal distribution, the following are true:

• Approximately 68% of the values are within ± 1 standard deviation from the mean
• Approximately 95% of the values are within ± 2 standard deviation from the mean
• Approximately 99.7% of the values are within ± 2 standard deviation from the mean

Question 18

Sample Covariance

Answer 18

Covariance measures the strength of the linear relatinoshp between two numerical variables (X and Y).

The Sample Covariance is…

Question 19

Sample Coefficient of Correlation

Answer 19