OPMT 1197
Business Statistics
Lecture 2: Measures of Variability
1. Below are the ages for a sample of students taken from two different sets.
Mean Median Mode
Set A 27 27 27 29 30 Close together
Set B 18 27 27 30 38 Very spread out
2. Below are three different sets of data. Calculate the range for each set of data.
Range
1 20 45 46 47 48 49 50
2 20 21 22 23 24 25 50
3 20 25 30 35 40 45 50
3. (a) Calculate the standard deviation of the ages for Set B. What is it for Set A?
2
xi x xi −
x (xi −
x )
Ages Mean Deviations Squared Deviations
18 28
27 28
27 28
30 28
38 28
Total
(b) What does it tell you about the ages of the students if the standard deviation is zero?
4. You have $5,000 to invest in the stock market. You have narrowed your choices to 2 different
stocks. Which stock is riskier?
National Bank Gold Seek
Average weekly closing price
$75 $0.80
(based on the past 52 weeks)
Standard Deviation $7.50 $2.40
Coefficient of Variation (CV)
Solutions:
1. 28, 27, 27 2. 30
3. (a) Set A: 1.4, B: 7.2 years (b) they are the same age (there is no variation in their ages)
4. 10%, 300% (Gold Seek is a very risky or volatile stock)
1
Business Statistics
Lecture 2: Measures of Variability
1. Below are the ages for a sample of students taken from two different sets.
Mean Median Mode
Set A 27 27 27 29 30 Close together
Set B 18 27 27 30 38 Very spread out
2. Below are three different sets of data. Calculate the range for each set of data.
Range
1 20 45 46 47 48 49 50
2 20 21 22 23 24 25 50
3 20 25 30 35 40 45 50
3. (a) Calculate the standard deviation of the ages for Set B. What is it for Set A?
2
xi x xi −
x (xi −
x )
Ages Mean Deviations Squared Deviations
18 28
27 28
27 28
30 28
38 28
Total
(b) What does it tell you about the ages of the students if the standard deviation is zero?
4. You have $5,000 to invest in the stock market. You have narrowed your choices to 2 different
stocks. Which stock is riskier?
National Bank Gold Seek
Average weekly closing price
$75 $0.80
(based on the past 52 weeks)
Standard Deviation $7.50 $2.40
Coefficient of Variation (CV)
Solutions:
1. 28, 27, 27 2. 30
3. (a) Set A: 1.4, B: 7.2 years (b) they are the same age (there is no variation in their ages)
4. 10%, 300% (Gold Seek is a very risky or volatile stock)
1
