Lesson 1 Flashcards
In what situations would absolute frequencies be more useful than relative frequencies?
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.
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?
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.
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?
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.
Real Estate investments are considered a good hedge against inflation. What does this tell you about the correlation between house prices and inflation?
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.
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?
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.
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)
2)
=($104,555 + $117,000 + $203,500 + $150,000 + $127,300 +$210,445) ! ($100,000 + $105,100 + $112,500 + $125,000)
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)
1)
= ($104,555 + $117,000 + $203,500 + $150,000 + $127,300) ÷ 5
= $702,355 ÷ 5
= $140,471
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: (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 %
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 (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.
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: (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.
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: (2)
Absolute frequency = 18; relative frequency = 0.15 = 18/n;
n = 18/0.15 = 120.
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: (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.
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: (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.
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 guide lesson 1 question 9
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: (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.
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: (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.
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: (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.
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: (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.
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: (3)
6(7,000) - 2(7,000) = $28,000
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: (3)
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: (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.
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: (1)
The mean is the calculated arithmetic average of the data values in a distribution.
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: (3)
Graphing the data shows a strong positive correlation, meaning the correlation coefficient (r) will be
close to +1.
