Question 1

What is the relationship among the mean, median and mode in a symmetric distribution?
A) All values are equal
B) Mean is always the smallest value
C) Mean is always the largest value
D) Mode is the largest value
E) Median is always the largest value

Accepted Answer

All values are equal

Question 2

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 kms with a standard deviation of 10,000 kms. Supplier B's tires have an average life of
100,000 kms with a standard deviation of 2,000 kms. Which of the following statements is true?
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

Accepted Answer

The life of Supplier B's tire is more predictable than the life of Supplier A's tires

Question 3

i. In a negatively skewed distribution, the mean is always greater than the median.
ii. In a negatively skewed distribution, the median occurs at the peak of the curve.
iii. In a positively skewed distribution, the mode is greater than the median.
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) (i) is a correct statement, but not (ii) or (iii).
E) (i), (ii) and (iii) are all false statements.

Accepted Answer

(i), (ii) and (iii) are all false statements.

Question 4

What is the relationship between the variance and the standard deviation?
A) Variance is the square root of the standard deviation
B) Variance is the square of the standard deviation
C) Variance is twice the standard deviation
D) No constant relationship between the variance and the standard deviation

Accepted Answer

Variance is the square of the standard deviation

Question 5

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 arithmetic mean would
Be an appropriate average.
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.

Accepted Answer

(i) and, (ii) are correct statements but (iii).

Question 6

i. In a positively skewed distribution, the mean is always greater than the median.
ii. In a negatively skewed distribution, the median occurs at the peak of the curve.
iii. In a negatively skewed distribution, the mode is greater than the median.
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) (i) is a correct statement, but not (ii) or (iii).
E) (i), (ii) and (iii) are all false statements.

Accepted Answer

(i) and, (iii) are correct statements but (ii).

Question 7

Which of the following measures of dispersion are based on deviations from the mean?
A) Variance
B) Standard deviation
C) Mean deviation
D) Mean deviation, standard deviation, and variance

Accepted Answer

Mean deviation, standard deviation, and variance

Question 8

The following printout is a summary of housing prices in Edmonton:  What can we determine from this printout?
A) The mean list price is less than both the median and modal prices
B) The median list price is the most representative as it is larger than the modal price and smaller than the mean price.
C) The modal price is affected by a few houses that must be priced very high
D) More than half of the houses are listed above $425,000.

Accepted Answer

The median list price is the most representative as it is larger than the modal price and

Question 9

i. In a positively skewed distribution, the mean is always greater than the median.
ii. In a negatively skewed distribution, the mode occurs at the peak of the curve.
iii. In a negatively skewed distribution, the mode is greater than the median.
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) (i) is a correct statement, but not (ii) or (iii).
E) (i), (ii) and (iii) are all false statements.

Accepted Answer

(i), (ii) and (iii) are all correct statements

Question 10

The following printout is a summary of number of bedrooms in homes for sale in Regina:  What can we determine from this printout?
A) The mean number of bedrooms is less than both the median and modal number.
B) The median number of bedrooms is the most representative as it is larger than the modal number and smaller than the mean number of bedrooms.
C) The modal number of bedrooms is affected by a few houses that must have a large number of bedrooms.
D) 75% of the houses have more than 3 bedrooms.

Accepted Answer

The mean number of bedrooms is less than both the median and modal number.

Question 11

Based on the graph below, how can we best describe the shape of this distribution? 
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) No variation
E) Bimodal

Accepted Answer

Positively skewed

Question 12

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.
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.

Accepted Answer

(i), (ii) and (iii) are all correct statements

Question 13

If a major sports star were to move into your neighbourhood, what would you expect to happen to
The neighbourhood's "average" income?
A) The mean income would decrease signiﬁcantly
B) The median income would increase signiﬁcantly
C) The modal income would increase signiﬁcantly
D) The mean income would increase signiﬁcantly, but the median income would stay almost the same as before
E) The standard deviation of the neighbourhood's income would get smaller

Accepted Answer

The mean income would increase signiﬁcantly, but the median income would stay almost

Question 14

What is the range for this sample of March electric bills amounts for all-electric homes of similar
Sizes (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175 and
$194.
A) $100
B) $130
C) $120
D) $112
E) $115

Accepted Answer

$120

Question 15

Rank the measures of dispersion in terms of their relative computational diﬃculty from least to most
Diﬃculty.
A) Mode, median, mean
B) Range, mean deviation, variance
C) Variance, mean deviation, range
D) There is no difference

Accepted Answer

Range, mean deviation, variance

Question 16

Based on the graph below, how can we best describe the shape of this distribution? 
A) Relatively symmetrical
B) Positively skewed
C) Negatively skewed
D) No variation
E) Bimodal

Accepted Answer

Relatively symmetrical

Question 17

What is a disadvantage of the range as a measure of dispersion?
A) Based on only two observations
B) Can be distorted by a large mean
C) Not in the same units as the original data
D) Has no disadvantage

Accepted Answer

Based on only two observations

Question 18

Based on the graph below, how can we best describe the shape of this distribution? 
A) Relatively symmetrical
B) Positively skewed
C) Negatively skewed
D) No variation
E) Bimodal

Accepted Answer

Positively skewed

Question 19

The ages of a sample of telephones used in a small town hotel were organized into the following
Table: 
What is the sample variance?
A) About 10.2
B) About 6.1
C) About 14.0
D) About 3.2
E) About 5.0

Accepted Answer

About 10.2

Question 20

The sum of the differences between sample observations and the sample mean is
A) Zero
B) The mean deviation
C) The range
D) The standard deviation
E) The mean

Accepted Answer

Zero

Quiz 3: Describing Data: Numerical Measures

What is the relationship among the mean, median and mode in a symmetric distribution?

i. In a negatively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the median occurs at the peak of the curve. iii. In a positively skewed distribution, the mode is greater than the median.

What is the relationship between the variance and the standard deviation?

i. In a positively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the median occurs at the peak of the curve. iii. In a negatively skewed distribution, the mode is greater than the median.

Which of the following measures of dispersion are based on deviations from the mean?

The following printout is a summary of housing prices in Edmonton: What can we determine from this printout?

i. In a positively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the mode occurs at the peak of the curve. iii. In a negatively skewed distribution, the mode is greater than the median.

The following printout is a summary of number of bedrooms in homes for sale in Regina: What can we determine from this printout?

Based on the graph below, how can we best describe the shape of this distribution?

If a major sports star were to move into your neighbourhood, what would you expect to happen to The neighbourhood's "average" income?

What is the range for this sample of March electric bills amounts for all-electric homes of similar Sizes (to the nearest dollar) : $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175 and $194.

Rank the measures of dispersion in terms of their relative computational diﬃculty from least to most Diﬃculty.

Based on the graph below, how can we best describe the shape of this distribution?

What is a disadvantage of the range as a measure of dispersion?

Based on the graph below, how can we best describe the shape of this distribution?

The ages of a sample of telephones used in a small town hotel were organized into the following Table: What is the sample variance?

The sum of the differences between sample observations and the sample mean is