Question 1

Referring to the printout below, describe the shape of the distribution of the corresponding histogram.

Accepted Answer

A)  Positively skewed 
B)  Negatively skewed 
C)  Perfectly symmetrical 
D)  Statistical 
A)  Positively skewed 
B)  Negatively skewed 
C)  Perfectly symmetrical 
D)  Statistical

Question 2

(i. If two sets of data are in different units, we can compare the dispersion by using coefficient of variation. (ii) A sample of the homes currently offered for sale revealed that the mean asking price is $75,900, the median $70,100 and the modal price is $67,200. The standard deviation of the distribution is $5,900. The Pearson's coefficient of skewness is 2.95
(iii) The coefficient of skewness is a measure of relative dispersion.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 3

The lengths of stay on the cancer floor of Community Hospital were organized into a frequency distribution. The mean length was 28 days, the median 25 days and the modal length 23 days. The standard deviation was computed to be 4.2 days. Determine the Pearson's coefficient of skewness.

Accepted Answer

A)  2.41 
B)  -2.41 
C)  2.14 
D)  -2.14 
A)  2.41 
B)  -2.41 
C)  2.14 
D)  -2.14

Question 4

A sample of five flooring installers, each carrying three types of flooring, was taken and the price per square metre (to the nearest cent) was recorded for each type of flooring, as shown in the table below.   (i) The range for laminate flooring is 0 or none.
(ii. The range for polyester carpet is $0.04 or 4 cents.
(iii) The mean deviation for laminate flooring is 0.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 5

(i. The research director of a large oil company conducted a study of the buying habits of consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be -0.30. (ii) The Pearson's coefficient of skewness (Sk) measures the amount of skewness and may range from -3.0 to +3.0. It is computed by subtracting the median from the mean, multiplying the result by 3 and dividing by standard deviation.
(iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the variance of this distribution were computed, it would be measured in hours squared

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 6

A telemarketing firm is monitoring the performance of its employees based on the number of sales per hour. One employee had the following sales for the last 20 hours   (i) The median for the distribution of number of sales per hour is 5 sales per hour.
(ii. The first quartile for the distribution of number of sales per hour is 4 sales per hour.
(iii) For the distribution of number of sales per hour, 50% of the observations are between 4 and 6.5.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 7

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics:   Describe the shape of the age of death distribution.

Accepted Answer

A)  Slight positive skewness 
B)  Slight negative skewness 
C)  Perfectly symmetrical 
D)  You cannot determine this from the data given 
E)  Strong negative skewness 
A)  Slight positive skewness 
B)  Slight negative skewness 
C)  Perfectly symmetrical 
D)  You cannot determine this from the data given 
E)  Strong negative skewness

Question 8

The weights of a sample of 100 boxes being shipped by Air France from Toronto to Paris are:   (i) Correct to two decimal places, the sample standard deviation is approximately 25.99.
(ii. Correct to two decimal places, the sample variance is approximately 675.25.

Accepted Answer

A)  (i) and(ii) are correct statements 
B)  (i) is a correct statement but not (ii). 
C)  (ii) is a correct statement but not (i). 
D)  (i) and (ii) are both false statements 
A)  (i) and(ii) are correct statements 
B)  (i) is a correct statement but not (ii). 
C)  (ii) is a correct statement but not (i). 
D)  (i) and (ii) are both false statements

Question 9

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 100,000 km with a standard deviation of 10,000 km. Supplier B's tires have an average life of 100,000 km with a standard deviation of 2,000 km. Which of the following statements is true?

Accepted Answer

A)  The two distributions of tire life are the same 
B)  On average, Supplier A's tires have a longer life then Supplier B's tires 
C)  The life of Supplier B's tire is more predictable than the life of Supplier A's tires 
D)  The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life 
E)  The life of Supplier A's tire is more predictable than the life of Supplier B's tires 
A)  The two distributions of tire life are the same 
B)  On average, Supplier A's tires have a longer life then Supplier B's tires 
C)  The life of Supplier B's tire is more predictable than the life of Supplier A's tires 
D)  The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life 
E)  The life of Supplier A's tire is more predictable than the life of Supplier B's tires

Question 10

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-seeConnectfordatafile.)   What were the median earnings for men for the years 1999-2008?

Accepted Answer

A)  $43,000 
B)  $44,400 
C)  $44,500 
D)  $44,600 
E)  $44,700 
A)  $43,000 
B)  $44,400 
C)  $44,500 
D)  $44,600 
E)  $44,700

Question 11

i. The sum of the deviations from the mean for the set of numbers 4, 9 and 5 will equal zero. ii. If there is an even number of ungrouped values, the median is found by arranging them from low to high and then determining the arithmetic mean of the two middle values.
iii. For salaries of $102,000, $98,000, $35,000, $106,000 and $101,000, the median would be an appropriate average.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 12

A box plot shows

Accepted Answer

A)  The mean and variance 
B)  The relative symmetry of a distribution for a set of data 
C)  The percentiles of a distribution 
D)  The deciles of a distribution 
E)  The location of the mean of a distribution 
A)  The mean and variance 
B)  The relative symmetry of a distribution for a set of data 
C)  The percentiles of a distribution 
D)  The deciles of a distribution 
E)  The location of the mean of a distribution

Question 13

What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, median of 12 and standard deviation of 6?

Accepted Answer

A)  + 2.5 
B)  - 2.5 
C)  + 0.83 
D)  - 0.83 
A)  + 2.5 
B)  - 2.5 
C)  + 0.83 
D)  - 0.83

Question 14

A sample of five flooring installers, each carrying three types of flooring, was taken and the price per square metre (to the nearest cent) was recorded for each type of flooring, as shown in the table below.   (i) The range for laminate flooring is 0 or none.
(ii. The standard deviation for nylon carpet is 6.64 cents
(iii) The range for nylon carpet is $0.12 or 12 cents.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 15

i. The mode is the value of the observation that appears most frequently. ii. A distribution that has the same shape on either side of the center is said to be symmetrical.
iii. Negatively skewed indicates that a distribution is not symmetrical. The long tail is to the left or in the negative direction.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 16

A company's human resource department was interested in the average number of years that a person works before retiring. The sample of size 11 follows:   (i) Based on the values of the arithmetic mean, median, and mode, the distribution is most likely symmetrical.
(ii. The arithmetic mean is 20.4.
(iii) The median is 21.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 17

The weights (in kilograms) of a group of crates being shipped to Panama are 95, 103, 110, 104, 105, 112 and 92. What is the mean deviation?

Accepted Answer

A)  5.43 kg 
B)  6.25 kg 
C)  0.53 kg 
D)  52.50 kg 
A)  5.43 kg 
B)  6.25 kg 
C)  0.53 kg 
D)  52.50 kg

Question 18

(i. The research director of a large oil company conducted a study of the buying habits of consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be + 0.30. (ii) Rainbow Trout, Inc., feeds fingerling trout in special ponds and markets them when they attain a certain weight. A group of 9 trout (considered the population) were isolated in a pond and fed a special food mixture called Grow Em Fast. At the end of the experimental period, the weights of the trout were (in grams): 124, 125, 123, 120, 124, 127, 125, 126 and 121. Another special mixture, Fatso 1B, was used in another pond. The mean of the population was computed to be 126.9 grams and the standard deviation was 1.20 grams. When these data are analysed, we discover that the food resulting in a more uniform weight is Fatso 1B.
(iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the variance of this distribution were computed, it would be measured in hours squared

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements. 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements, but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 19

The coefficient of variation generally lies between what two values?

Accepted Answer

A)  - 1 and + 1 
B)  - 3 and + 3 
C)  0% and 100% 
D)  Unlimited values 
A)  - 1 and + 1 
B)  - 3 and + 3 
C)  0% and 100% 
D)  Unlimited values

Question 20

A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?

Accepted Answer

A)  $100 and $200 
B)  $85 and $105 
C)  $205 and $220 
D)  $110 and $190 
A)  $100 and $200 
B)  $85 and $105 
C)  $205 and $220 
D)  $110 and $190

Referring to the printout below, describe the shape of the distribution of the corresponding histogram.

The lengths of stay on the cancer floor of Community Hospital were organized into a frequency distribution. The mean length was 28 days, the median 25 days and the modal length 23 days. The standard deviation was computed to be 4.2 days. Determine the Pearson's coefficient of skewness.

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics: Describe the shape of the age of death distribution.

The weights of a sample of 100 boxes being shipped by Air France from Toronto to Paris are: (i) Correct to two decimal places, the sample standard deviation is approximately 25.99. (ii. Correct to two decimal places, the sample variance is approximately 675.25.

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-seeConnectfordatafile.) What were the median earnings for men for the years 1999-2008?

A box plot shows

What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, median of 12 and standard deviation of 6?

The weights (in kilograms) of a group of crates being shipped to Panama are 95, 103, 110, 104, 105, 112 and 92. What is the mean deviation?

The coefficient of variation generally lies between what two values?

A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

Exam 3: Describing Data: Numerical Measures

Referring to the printout below, describe the shape of the distribution of the corresponding histogram.

The lengths of stay on the cancer floor of Community Hospital were organized into a frequency distribution. The mean length was 28 days, the median 25 days and the modal length 23 days. The standard deviation was computed to be 4.2 days. Determine the Pearson's coefficient of skewness.

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics: Describe the shape of the age of death distribution.

The weights of a sample of 100 boxes being shipped by Air France from Toronto to Paris are: (i) Correct to two decimal places, the sample standard deviation is approximately 25.99. (ii. Correct to two decimal places, the sample variance is approximately 675.25.

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-seeConnectfordatafile.) What were the median earnings for men for the years 1999-2008?

A box plot shows

What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, median of 12 and standard deviation of 6?

The weights (in kilograms) of a group of crates being shipped to Panama are 95, 103, 110, 104, 105, 112 and 92. What is the mean deviation?

The coefficient of variation generally lies between what two values?

A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters