Quiz 3 Measures of Dispersion

Question 1

Here are 10 gross income multipliers. 5.9 6.2 5.7 6.3 6.4 6.0 5.5 5.8 6.3 6.9 What is the sum of the differences between the mean and the variants (X – X)?

Answer 1

3.2. You have to take each of the GIMs and determine how much each one differs from the mean we just found (6.1). For example: the first number is 5.9. 6.1 - 5.9 = .2. The second number is 6.2. 6.2 - 6.1 = .1. We are looking for absolute numbers – how far is each GIM away from the mean – regardless of whether it is a positive or negative number. Calculate each of these 10 differences and then add them up. The answer is 3.2.

Question 2

In a normal distribution, approximately ____ % of the observations fall within two standard deviations (+ or -) from the mean.

Answer 2

95

Question 3

Here are 14 numbers. 235 218 266.5 298 222 246 264 255 274 261 277 214 256 239 What is the standard deviation?

Answer 3

24.3. Once you have calculated the mean, enter g s Answer is 24.30.

Question 4

“The number of values in a calculation of a statistic that are free to vary” is the definition of

Answer 4

degrees of freedom

Question 5

“A symmetrical, bell-shaped curve that represents the distribution of a population of certain types of measurements or the frequency distribution of all possible means in large samples that may have been drawn from an unknown population distribution” is the definition of

Answer 5

Normal curve

Question 6

“The amount a variable’s value differs from the mean or some other benchmark” is the definition of

Answer 6

deviation

Question 7

Here are 8 land sales. $45,000 $37,000 $34,500 $48,000 $41,000 $47,500 $39,500 $51,000 What is the sum of the differences between the mean and the variants?

Answer 7

39500. You have to take each of the GIMs and determine how much each one differs from the mean we just found (42,938). For example: the first number is 45,000. 45,000 – 42,938 = 2,062. The second number is 37,000. 42,938 – 37,000 = 5,938. We are looking for absolute numbers – how far is each GIM away from the mean – regardless of whether it is a positive or negative number. Calculate each of these 10 differences and then add them up. The answer is 39,500.

Question 8

A large sample consists of ______ or more observations.

Answer 8

30

Question 9

“The result of a sample selection process where all members of a population or population stratum have the same probability of being selected” is the definition of

Answer 9

random sample

Question 10

An appraiser calculates the mean of a set of numbers, and then subtracts the mean from each number, adds up these differences without regard to sign, and divides this sum by the number of items. What has the appraiser calculated?

Answer 10

average deviation

Question 11

Here are 16 numbers. 43 56 38 61.5 46 59 35 67.5 50 52 41 44 63 49 53 46 What is the mean of the numbers?

Answer 11

50.25. Use your 12C: f CLEAR S 43 S+ 56 S+ 38 S+ 61.5 S+ 46 S+ 59 S+ 35 S+ 67.5 S+ 50 S+ 52 S+ 41 S+ 44 S+ 63 S+ 49 S+ 53 S+ 46 S+ g Answer is 50.25.

Question 12

In a normal distribution, approximately ____ % of the observations fall within one standard deviation (+ or -) from the mean.

Answer 12

68

Question 13

“A theoretical distribution often approximated in real-world situations. It is symmetrical and bell-shaped” is the definition of

Answer 13

normal distribution

Question 14

The deviation as shown on a chart would be measured by the difference from the observation to the mean measured by a line that runs __________to the line of the mean.

Answer 14

perpendicular

Question 15

Here are 10 gross income multipliers. 5.9 6.2 5.7 6.3 6.4 6.0 5.5 5.8 6.3 6.9 What is the average absolute deviation?

Answer 15

0.32. If the total of the differences (deviations) is 3.2 and there are 10 deviations; then the average absolute deviation is 3.2 ÷ 10 = 0.32.

Question 16

Here are 8 land sales. $45,000 $37,000 $34,500 $48,000 $41,000 $47,500 $39,500 $51,000 What is the range?

Answer 16

16500. $51,000 - $34,500 = $16,500.

Question 17

Here are 10 gross income multipliers. 5.9 6.2 5.7 6.3 6.4 6.0 5.5 5.8 6.3 6.9 What is the mean?

Answer 17

6.1. Use your 12C: f CLEAR S 5.9 S+ 6.2 S+ 5.7 S+ 6.3 S+ 6.4 S 6.0 S+ 5.5 S+ 5.8 S+ 6.3 S+ 6.9 S+ g Answer is 6.1.

Question 18

The difference between an observation and the measure of central tendency for that array, without regard as to the sign of the difference, is the

Answer 18

absolute deviation

Question 19

Here are 14 numbers. 235 218 266.5 298 222 246 264 255 274 261 277 214 256 239 What is the mean of the numbers?

Answer 19

251.82. F CLEAR S 235 S+ 218 S+ 266.5 S+298 S+ 222 S+ 246 S+ 264 S+255 S+ 274 S+ 261 S+ 277 S+ 214 S+ 256 S+ 239 S+ g Answer is 251.82.

Question 20

In a normal distribution, approximately ____ % of the observations fall within three standard deviations(+ or -) from the mean.

Answer 20

99

Question 21

Here are 8 land sales. $45,000 $37,000 $34,500 $48,000 $41,000 $47,500 $39,500 $51,000 What is the mean?

Answer 21

42938. Use your 12C: f CLEAR S 45,000 S+ 37,000 S+ 34,500 S+ 48,000 S+ 41,000 S+ 47,500 S+ 39,500 S+ 51,000 S+ g Answer is $42,938.

Question 22

Here are eight land sales. $45,000 $37,000 $34,500 $48,000 $41,000 $47,500 $39,500 $51,000 What is the average absolute deviation?

Answer 22

4937.5. The first step is to calculate the mean (average) of the sales. The next step is to calculate the amount that each sale deviates from the mean. However, those answers have both positive and negative numbers. So we need to convert those numbers to the absolute value - the number without the negative sign on the negative numbers. The next step is to total the absolute deviations. The total of the absolute deviations is then divided by the number of sales, which results in the average absolute deviation from the mean in the sample of sales. The total of the absolute deviations in this case is $39,500. Divide that by 8 and it equals 4,937.50.

Question 23

Here are 8 land sales. $45,000 $37,000 $34,500 $48,000 $41,000 $47,500 $39,500 $51,000 What is the range?

Answer 23

$16,500

Question 24

Here are 16 numbers. 43 56 38 61.5 46 59 35 67.5 50 52 41 44 63 49 53 46 What is the standard deviation?

Answer 24

9.33. If you still have all the information in your 12C after you found the mean in the last problem, you can find the Standard Deviation of those 16 numbers in one more simple step: press g s. The answer is 9.33

Question 25

“The difference between the highest and lowest values in a set of numbers” defines

Answer 25

range

Question 26

Measures of dispersion would include all of the following

Answer 26

standard deviation, range, average deviation

Question 27

“A sample produced by an unscientific, non-random process”, for example a sample based on an appraiser’s judgment or a convenience sample is a ____________ sample.

Answer 27

nonprobability

Question 28

Which of the following can be used in the analysis of dispersion?

Answer 28

range