# Mathematics

1.

Consider the following population data:

21 27 11 13 7

a. Calculate the range.

Range

b.

Calculate MAD. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

c.

Calculate the population variance. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population variance

d.

Calculate the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population standard deviation

rev: 07_31_2013_QC_32713

2.

Consider the following sample data:

x 11 13 15 17 19

y 19 17 15 13 11

a.

Calculate the covariance between the variables. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Covariance

b-1.

Calculate the correlation coefficient. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Correlation coefficient

b-2. Interpret the correlation coefficient.

There is

relationship between x and y.

rev: 07_31_2013_QC_32713

3.

Consider the following observations from a population:

88 235 73 138 138 71 229 153 73

a. Calculate the mean and median. (Round “mean” to 2 decimal places.)

Mean

Median

b.

Select the mode. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.)

138

71

88

73

153

229

235

rev: 07_31_2013_QC_32713

4.

A manager of a local retail store analyzes the relationship between advertising and sales by reviewing the store’s data for the previous six months.

Advertising (in \$100s) Sales (in \$1,000s)

174 144

57 45

56 44

55 43

212 136

210 134

a.

Calculate the mean of advertising and the mean of sales. (Round your answers to 2 decimal places.)

Mean

Sales

b.

Calculate the standard deviation of advertising and the standard deviation of sales. (Round your answers to 2 decimal places.)

Standard Deviation

Sales

Covariance

c-2.

Interpret the covariance between advertising and sales.

No correlation

Negative correlation

Positive correlation

d-1.

Correlation coefficient

d-2.

Interpret the correlation coefficient between advertising and sales.

No correlation

Weak negative correlation

Strong positive correlation

Strong negative correlation

Weak positive correlation

rev: 07_31_2013_QC_32713

5.

An investment strategy has an expected return of 12 percent and a standard deviation of 8 percent. Assume investment returns are bell shaped.

a.

How likely is it to earn a return between 4 percent and 20 percent? (Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Probability

b.

How likely is it to earn a return greater than 20 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Probability

c.

How likely is it to earn a return below −4 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Probability

rev: 02_26_2014_QC_44958, 07_12_2014_QC_5

6.

The following relative frequency distribution was constructed from a population of 400. Calculate the population mean, the population variance, and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Class Relative Frequency

−20 up to −10 0.14

−10 up to 0 0.22

0 up to 10 0.32

10 up to 20 0.32

Population mean

Population variance

Population standard deviation

rev: 07_31_2013_QC_32713

7.

Consider the following frequency distribution.

Class Frequency

2 up to 4 19

4 up to 6 61

6 up to 8 79

8 up to 10 19

a.

Population mean

b.

Calculate the population variance and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Population variance

Population standard deviation

rev: 07_31_2013_QC_32713

8.

A data set has a mean of 1,000 and a standard deviation of 50.

a.

Using Chebyshev’s theorem, what percentage of the observations fall between 800 and 1,200? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Percentage of observations

b.

Using Chebyshev’s theorem, what percentage of the observations fall between 750 and 1,250? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Percentage of observations

rev: 07_31_2013_QC_32713

9.

Consider the following returns for two investments, A and B, over the past four years:

Investment 1: 2% 14% –3% 15%

Investment 2: 13% 12% –18% 14%

a-1.

Calculate the mean for each investment. (Round your answers to 2 decimal places.)

Mean

Investment 1 percent

Investment 2 percent

a-2.

Which investment provides the higher return?

Investment 2

Investment 1

b-1.

Calculate the standard deviation for each investment. (Round your answers to 2 decimal places.)

Standard

Deviation

Investment 1

Investment 2

b-2.

Which investment provides less risk?

Investment 1

Investment 2

c-1.

Given a risk-free rate of 1.3%, calculate the Sharpe ratio for each investment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Sharpe Ratio

Investment 1

Investment 2

c-2. Which investment has performed better?

Investment 2

Investment 1

rev: 07_31_2013_QC_32713, 11_10_2013_QC_38348

10.

Scores on the final in a statistics class are as follows.

94 45 95 82 96 100 100 119 110 80

105 119 60 94 92 85 107 89 105 90

a.

Calculate the 25th, 50th, and 75th percentiles. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

25th percentile

50th percentile

75th percentile

b-1.

Calculate the IQR, lower limit and upper limit to detect outliers. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

IQR

Lower limit

Upper limit

b-2. Are there any outliers?

Yes

No

rev: 07_31_2013_QC_32713, 09_13_2013_QC_34880, 10_31_2013_QC_38175, 03_03_2014_QC_44705, 09_24_2014_QC_54188, 02_26_2015_QC_CS-5733

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