Lesson 1

Question 1

In what situations would absolute frequencies be more useful than relative frequencies?

Answer 1

Absolute frequencies are more useful for comparison than relative frequencies where the sample size
is small and the relative comparison may not be as meaningful.

Question 2

A condo developer commissions a study about average family size. The study reports that the average family size is 2.5 people so she builds 300 units with 2 bedrooms and a den. However, the units don’t see well because most buyers complain that the condos are either too small or too large for their needs. What went wrong?

Answer 2

An average (or mean) measure may not always be representative of a distribution. In this example, the
average size of households was determined to be 2.5, however, a household cannot have 2.5 people in
actuality because household size is a discrete variable. It may have been more effective for the developer
to use the mode size or examine the relative distribution of household size to determine what to build.

Question 3

If the range for distribution is greater than the range for distribution 2, what can you conclude about their respective Std. Dev. values? Can you conclude the same thing about their coefficient of variation?

Answer 3

The standard deviation is a measure of the dispersion of a distribution. While the range of a distribution
may have a significant effect on its standard deviation, the actual distribution will determine the size of
the standard deviation. If one distribution has a greater range than another, it is likely that it will have
a greater standard deviation. However, if the distribution with the larger range is more tightly
distributed around the mean with an outlier resulting in a large range, the standard deviation may be
smaller than that of a distribution that is more widely dispersed but with a slightly smaller range. The
COV is a ratio of the standard deviation divided by the mean, and therefore, the range does not tell us
very much about this value.

Question 4

Real Estate investments are considered a good hedge against inflation. What does this tell you about the correlation between house prices and inflation?

Answer 4

If real estate is in fact a good hedge against inflation, housing prices and inflation must be (very)
positively correlated. As such, when inflation increases, so would house prices. For example, let’s
examine a house bought for $200,000 in 1990. Because housing prices should rise with inflation, the
same house will be worth more today. However, because of inflation, if the original $200,000 is held
in cash since 1990, it is worth less today as it has less purchasing power. Therefore, by holding onto
the real estate, you have hedged against inflation, and retained value in your investment. Whether or
not real estate is actually a good hedge against inflation is a very debatable topic.

Question 5

Some skeptics claim that Canada adopted the metric system to hide price inflation. How does a $0.02/litre increase in gas prices relate to a $0,020/gallon increase in percentage terms (assume there are 4 liters per gallon)? Similarity, why is smoke salmon often sold on the basis of price per 100 grams instead of per kilogram?

Answer 5

By lowering the unit size, the price per unit appears lower. Larger relative price increases may be
hidden. For example, a 20 cent per litre increase in gas prices doesn’t seem like much, but an
equivalent 80 cent overnight increase per gallon would seem a lot steeper, even though both are actually
the same percentage increase. If both increased by 20 cents, the increase in the per gallon rate is only
25% or one-quarter the increase in the price per litre.
Similarly, if smoked salmon is $20/pound, this would be $44/kilogram. It is more enticing to sell it
as $4.40 per 100 grams, as to the casual shopper this might seem cheaper than $20/pound. These are
both examples of how statistics can be manipulated in order to mislead.

Question 6

Jonny, a real estate developer, has recently developed a large tract of land near Scotch Creek,. Sales have been slow thus far. Although there are 102 beautiful lots available for purchase, only ten have sold. the following are observations of the prices for the sales completed thus far:
Lot 1 (X1) = $104,555               Lot 40 (X6) = $210,445
Lot 5 (X2) = $117,000              Lot 41 (X7) = $100,000
Lot 21 (X3) = $203,500           Lot 42 (X8) = $105,100
Lot 22 (X4) = $150,000           Lot 98 (X9) = $112,500
Lot 35 (X5) = $127,300            Lot 99 (X10) = $ 125,000

Calculate the following Sums (lesson 1 MC 1)

Answer 6

2)

=($104,555 + $117,000 + $203,500 + $150,000 + $127,300 +$210,445) ! ($100,000 + $105,100 + $112,500 + $125,000)

Question 7

Jonny, a real estate developer, has recently developed a large tract of land near Scotch Creek,. Sales have been slow thus far. Although there are 102 beautiful lots available for purchase, only ten have sold. the following are observations of the prices for the sales completed thus far:
Lot 1 (X1) = $104,555               Lot 40 (X6) = $210,445
Lot 5 (X2) = $117,000              Lot 41 (X7) = $100,000
Lot 21 (X3) = $203,500           Lot 42 (X8) = $105,100
Lot 22 (X4) = $150,000           Lot 98 (X9) = $112,500
Lot 35 (X5) = $127,300            Lot 99 (X10) = $ 125,000

Calculate the following Sums (lesson 1 MC 2)

Answer 7

1)
= ($104,555 + $117,000 + $203,500 + $150,000 + $127,300) ÷ 5

= $702,355 ÷ 5

= $140,471

Question 8

The following are hypothetical data for residential real estate sales activity”
Year Sales
1 13,850
2 14,458
3 14,008
4 15,839
5 16,445
Which one of the following statements is TRUE?
1) The % change between Year 1 and 2 is larger than year 4 and 5, and the absolute change between Year 1 and 2 is smaller than year 4 and 5.
2) The % change between Year 1 and 2 is smaller than year 4 and 5, and the absolute change between Year 1 and 2 is larger than year 4 and 5.
3) The % change between Year 1 and 2 is smaller than year 4 and 5, and the absolute change between Year 1 and 2 is smaller than year 4 and 5.
4)The % change between Year 1 and 2 is larger than year 4 and 5, and the absolute change between Year 1 and 2 is larger than year 4 and 5.

Answer 8

Answer: (4)

Absolute Change (year 1 to 2) = 14,458 - 13,850 = $608

Percentage Change (year 1 to 2) = 100 × ( 608/13,850) = 4.4%

Absolute Change (year 4 to 5) = 16,445 - 15,839 = $606

Percentage Change (year 4 to 5) = 100 × (606/15,839 ) = 3.8 %

Question 9

Relate to Lesson 1 data above MC Question 4

What is the relative frequency of 42 as the number of days?

1) 0.1
2) 5
3) 6
4) 0.12

Answer 9

Answer (4)
42 days was the difference between the listing and sale date on 6 out of 50 instances. Therefore, the
relative frequency of 42 days is = 0.12.

Question 10

Relate to Lesson 1 data above MC Question 4

What is the relative frequency of the group 38-43 days?

1) 0.24
2) 0.34
3) 0.36
4) 0.40

Answer 10

Answer: (3)
There were 18 instances where the difference between the listing date and the sale date was between 38-
43 days. Therefore, the relative frequency for this group is = 0.36.

Question 11

The relative frequency of a dataset group is determined to be 0.15 while the absolute frequency is 18 (for the same group). What is the total number of observations in the dataset?

1) 100
2) 120
3) 90
4) none of the above

Answer 11

Answer: (2)
Absolute frequency = 18; relative frequency = 0.15 = 18/n;
n = 18/0.15 = 120.

Question 12

Which of the following variables is discrete?

a. Year built of the house
b. Price of the house
c. Length of the house
d. Number of fireplaces

1) a and b
2) b and c
3) d and b
4) none of the above

Answer 12

Answer: (1)
A discrete variable is one which can assume only a limited amount of values. Age expressed as year
the house was built can only take on whole number values (1968, 2001, etc.). The number of fireplaces
can only be expressed as 0, 1, 2, etc.

Question 13

When writing the following news headlines, the writers used statistics to make an assertion. In which of the cases was the variable measured a continuous variable?
A. “Real estate markets booming: the number of sales triples”
B. “ Americans gaining weight every year: obesity has doubles among adults”
C. “Corporate profits going down”
D. “mad cow disease reduces the number of animals in continental Europe”
E. “Salaries of real estate salepeople greater than ever”

1) A, B, C, and E
2) C and E
3) A and D
4) Only E

Answer 13

Answer: (2)
The number of sales, the number of animals and obese people are discrete variables; i.e., they can only
be whole numbers. Dollar profits, and dollar salaries are continuous variables.

Question 14

The following is a distribution of selling prices for 12 homes:
$100,000 $95,000 $100,000 $540,000
$155,000 $96,000 $155,000 $133,000
$120,000 $135,000 $80,000 $175,000

What is the standard deviation for the distribution of sale prices?

1) $157,000
2) $141,202
3) $14,1420,166,667
4) $118,828

Answer 14

answer guide lesson 1 question 9

Question 15

For a given distribution and a given mean, an increase in the value of the std dev will:

1) decrease the representativeness of the arithmetic mean
2) have no impact on the representativeness of the arithmetic mean
3) improve the representativeness of the arithmetic mean
4) have an ambiguous impact on the representativeness of the arithmetic mean

Answer 15

Answer: (1)
An increase in the value of the standard deviation characterizes a data series that is more variant, or
more spread out. When the data is more spread out around an arithmetic mean and the quality, or
representativeness, decreases.

Question 16

lesson 1 MC 11 diagrams

which of the distributions would have a median value that is less than the mean value?

1) A and B
2) B and D
3) C only
4) C and D

Answer 16

Answer: (1)
In order for the median to be less than the mean the data must be skewed to the right. This is the case
in distributions (A) and (B). When a number of very large data points are used in determining the mean
it will increase the mean thus making it higher than the median.

Question 17

The std dev is:

1) the difference between the min and max values in a distribution
2) the square of variance
3) a measure of distribution of data around the mean of distribution, measured in the same units as the original variable
4) a measure of distribution of data around the mean of the distribution, measures in % terms

Answer 17

Answer: (3)
Standard deviation is a measure of dispersion of data around the mean of the distribution, measured in
the same units as the original variable.

Question 18

Price = 35,000 + 25,000 x #of rooms x #of bathrooms

A house with 5 rooms and 3 bathrooms would sell for:

1) $149,000 more than a house with 2 rooms and 1 bath
2) $32,000 more than a house with 4 rooms and 2 baths
3) the same as a house with 4 rooms and 4 baths
4) $19,000 less than a house with 6 rooms and 1 bath

Answer 18

Answer: (2)
A house with 5 rooms and 3 bathrooms would sell for: 35,000 + 25,000(5) + 7,000(3) = $181,000
A house with 2 rooms and 1 bathroom would sell for $92,000.
A house with 4 rooms and 2 bathrooms would sell for $149,000.
A house with 4 rooms and 4 bathrooms would sell for $163,000.
A house with 6 rooms and 1 bathroom would sell for $192,000.

Question 19

Price = 35,000 + 25,000 x #of rooms x #of bathrooms

An increase in the number of baths from 2 to 6 would increase the sale price by:

1) $7,000
2) $35,000
3) $28,000
4) $42,000

Answer 19

Answer: (3)

6(7,000) - 2(7,000) = $28,000

Question 20

Last year a small realty firm paid its four clerks $35,000 each, five junior agents $55,000 each, five senior agents $90,000 each and the firms manager $340,000.

What are the mean and median salaries paid at the firm?

1) Mean: $80,333.33; Median $90,000
2) Mean: $55,000; Median $80,333.33
3) Mean: $80,333.33; Median $55,000
4) Mean: $90,000; Median $55,000

Answer 20

Answer: (3)

Question 21

Last year a small realty firm paid its four clerks $35,000 each, five junior agents $55,000 each, five senior agents $90,000 each and the firms manager $340,000.

Suppose the firm hires another managing partner. His salary is $340,000 per year. What effect will this have in the mean and the median salaries of he group, respectively?

1) No change, no change
2) increase, no change
3) no change, increase
4) increase, increase

Answer 21

Answer: (2)
Intuitively, the mean will increase when a new person is hired with a salary more than the original
average. But the median will not change because the middle value will still be $55,000.

Question 22

The mean is:

1) The calculated arithmetic average of the data values in a distribution
2) the middle data value in a distribution
3) a measure of distribution in a dataset
4) the value that occurs most frequently in a distribution

Answer 22

Answer: (1)

The mean is the calculated arithmetic average of the data values in a distribution.

Question 23

The following provides information on the price and number of stories of 8 apartment buildings:
Xi Yi
Stories Sale Price
1 $1,000,000
3 $2,000,000
4 $4,000,000
6 $4,000,000
8 $5,000,000
9 $7,000,000
11 $8,000,000
14 $9,000,000
What is the linear correlation coefficient between X and Y?
1) Close to 0
2) Close to -1
3) Close to `1
4) Close to 0.5

Answer 23

Answer: (3)
Graphing the data shows a strong positive correlation, meaning the correlation coefficient (r) will be
close to +1.