STAT 200 Homework 2 Solutions

Question 1: Frequency Distribution, Relative Frequency Distribution, and Cumulative Frequency Distribution

1. The median incomes of females in each state of the United States, including the District of Columbia and Puerto Rico, are given in Table 1 and in the “STAT 200 – Homework 2 Data Sets.xlsx” file ("Median income of females," 2013). Create a frequency distribution, relative frequency distribution, and cumulative frequency distribution using exactly 8 (no more, no less) classes.

$31,862 $40,550 $36,048 $30,752 $41,817 $40,236 $47,476 $40,500

$60,332 $33,823 $35,438 $37,242 $31,238 $39,150 $34,023 $33,745

$33,269 $32,684 $31,844 $34,599 $48,748 $46,185 $36,931 $40,416

$29,548 $33,865 $31,067 $33,424 $35,484 $41,021 $47,155 $32,316

$42,113 $33,459 $32,462 $35,746 $31,274 $36,027 $37,089 $22,117

$41,412 $31,330 $31,329 $33,184 $35,301 $32,843 $38,177 $40,969

$40,993 $29,688 $35,890 $34,381

Table 1

2. Create a histogram and relative frequency histogram for the data in Table 1 (i.e. Problem 1). Describe the shape and any findings you can from the graph.

3. Create an ogive for the data in Table 1 (i.e. Problem 1). Describe any findings you can from the graph.

4. Table 2 (also in the “STAT 200 – Homework 2 Data Sets.xlsx” file) contains the value of a rental house and the amount of rental income in a year that the house brings in ("Capital and rental,"2013). Create a scatter plot and state if there is a relationship between the value of the house and the annual rental income.

Value Rental Value Rental Value Rental Value Rental

81000 6656 77000 4576 75000 7280 67500 6864

95000 7904 94000 8736 90000 6240 85000 7072

121000 12064 115000 7904 110000 7072 104000 7904

135000 8320 130000 9776 126000 6240 125000 7904

145000 8320 140000 9568 140000 9152 135000 7488

165000 13312 165000 8528 155000 7488 148000 8320

178000 11856 174000 10400 170000 9568 170000 12688

200000 12272 200000 10608 194000 11232 190000 8320

214000 8528 208000 10400 200000 10400 200000 8320

240000 10192 240000 12064 240000 11648 225000 12480

289000 11648 270000 12896 262000 10192 244500 11232

325000 12480 310000 12480 303000 12272 300000 12480

Table 2

5. The economic crisis of 2008 affected many countries, though some more than others. Some people in Australia have claimed that Australia was not negatively impacted by the crisis. The bank assets (in billions of Australia dollars (AUD)) of the Reserve Bank of Australia (RBA) for the time period of March 2007 through March 2013 are contained in Table 3 and in the “STAT 200 – Homework 2 Data Sets.xlsx” file. Create a timeseries plot and interpret any findings.

Question 2: Histogram and Relative Frequency Histogram

Date Assets in

Billions of AUD Date Assets in

Billions of AUD Date Assets in

Billions of AUD

Mar-06 96.9 Sep-08 101.5 Mar-11 75.7

Jun-06 107.4 Dec-08 158.8 Jun-11 75.9

Sep-06 107.2 Mar-09 118.7 Sep-11 75.2

Dec-06 116.2 Jun-09 111.9 Dec-11 87.9

Mar-07 123.7 Sep-09 87 Mar-12 91

Jun-07 134 Dec-09 86.1 Jun-12 90.1

Sep-07 123 Mar-10 83.4 Sep-12 83.9

Dec-07 93.2 Jun-10 85.7 Dec-12 95.8

Mar-08 93.7 Sep-10 74.8 Mar-13 90.5

Jun-08 105.6 Dec-10 76

6.The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in Table 4 and in the “STAT 200 – Homework 2 Data Sets.xlsx” file (Lee,1994).

a.) Find the Mean.

b.) Find the Median

c.) Find the Mode.

Show your work (you can submit an Excel file to satisfy this requirement), and clearly indicate your final answer.

River Length (km)

Ashburton 90

Ashley 97

Clarence 209

Clutha 322

Conway 48

Hurunui 138

Kakanui 64

Ophi 80

Pareora 56

Rakaia 145

Rangitata 121

Selwyn 95

Shag 72

Taieri 288

Waiau 169

Waihao 64

Waimakariri 161

Waipara 64

Waitaki 209

Table 4

7.State which type of measurement scale each represents, and then which center measures can be used for the variable?

a.) You collect data on the height of plants using a new fertilizer.

b.) You collect data on the cars that people drive in Campbelltown, Australia.

c.) You collect data on the temperature at different locations in Antarctica.

d.) You collect data on the first, second, and third winner in a beer competition.

8. An employee at Coconino Community College (CCC) is evaluated based on goal setting and accomplishments toward goals, job effectiveness, competencies, and CCC core values. Suppose for a specific employee, goal 1 has a weight of 20%, goal 2 has a weight of 20%, goal 3 has a weight of 10%, job effectiveness has a weight of 25%, competency 1 has a goal of 4%, competency 2 has a goal has a weight of 3%, competency 3 has a weight of 3%, competency 4 has a weight of 5%, and core values has a weight of 10%. Suppose the employee has scores of 2.0 for goal 1, 2.0 for goal 2, 4.0 for goal 3, 3.0 for job effectiveness, 2.0 for competency 1, 3.0 for competency 2, 2.0 for competency 3, 3.0 for competency 4, and 4.0 for core values. This data is summarized in the “STAT 200 – Homework 2 Data Sets.xlsx” file.

a.) Find the weighted average score for this employee.

b.) If an employee that has a score less than 2.5, they must have a Performance Enhancement Plan written. Does this employee need a plan? Show your work (you can submit an Excel file to satisfy this requirement), and clearly indicate your final answer.

9. The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in Table 4 (in Problem 6 above) and in the “STAT 200 – Homework 2 Data Sets.xlsx” file (Lee,1994).

a.) Find the Range.

b.) Find the Variance.

c.) Find the Standard Deviation.

Show your work (you can submit an Excel file to satisfy this requirement), and clearly indicate your final answer.

10.Print-O-Matic printing company spends specific amounts on fixed costs every month. The costs of those fixed costs are in Table 5 and in the “STAT 200 – Homework 2 Data Sets.xlsx” file.

a.) Find the Median.

b.) Find the Mean.

c.) Find the Range.

d.) Find the Variance

e.) Find the Standard Deviation.

Show your work (you can submit an Excel file to satisfy this requirement), and clearly indicate your final answer.

Monthly charges Monthly cost ($)

Bank charges 482

Cleaning 2208

Computer expenses 2471

Lease payments 2656

Postage 2117

Uniforms 2600