Find the variance and standard deviation.


STAT 200 Homework Problems

2.2.2

The median incomes of females in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #2.2.10 (“Median income of,” 2013). Create a frequency distribution, relative frequency distribution, and cumulative frequency distribution using 7 classes.

Table #2.2.10: Data of Median Income for Females

$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

2.2.6

Create a histogram and relative frequency histogram for the data in table #2.2.10. Describe the shape and any findings you can from the graph.

2.2.10

Create an ogive for the data in table #2.2.10. Describe any findings you can from the graph.

2.3.4

Table #2.3.7 contains the value of the 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.

Table #2.3.7: Data of House Value versus Rental

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

2.3.8

The economic crisis of 2008 affected many countries, though some more than others. Some people in Australia have claimed that Australia wasn’t hurt that badly from 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 #2.3.11 (“B1 assets of,” 2013). Create a time-series plot and interpret any findings.

Table #2.3.11: Data of Date versus RBA Assets

Date Assets in billions of AUD
Mar-2006 96.9
Jun-2006 107.4
Sep-2006 107.2
Dec-2006 116.2
Mar-2007 123.7
Jun-2007 134.0
Sep-2007 123.0
Dec-2007 93.2
Mar-2008 93.7
Jun-2008 105.6
Sep-2008 101.5
Dec-2008 158.8
Mar-2009 118.7
Jun-2009 111.9
Sep-2009 87.0
Dec-2009 86.1
Mar-2010 83.4
Jun-2010 85.7
Sep-2010 74.8
Dec-2010 76.0
Mar-2011 75.7
Jun-2011 75.9
Sep-2011 75.2
Dec-2011 87.9
Mar-2012 91.0
Jun-2012 90.1
Sep-2012 83.9
Dec-2012 95.8
Mar-2013 90.5

3.1.2

The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in table #3.1.8 (Lee, 1994). Find the mean, median, and mode.

Table #3.1.8: Lengths of Rivers (km) Flowing to Pacific Ocean

River Length (km) River Length (km)
Clarence 209 Clutha 322
Conway 48 Taieri 288
Waiau 169 Shag 72
Hurunui 138 Kakanui 64
Waipara 64 Rangitata 121
Ashley 97 Ophi 80
Waimakariri 161 Pareora 56
Selwyn 95 Waihao 64
Rakaia 145 Waitaki 209
Ashburton 90

3.1.8

State which type of measurement scale each represents, and then which center measures can be use 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.

3.1.12

An employee at Coconino Community College (CCC) is evaluated based on goal setting and accomplishments toward goals, job effectiveness, competencies, 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. Find the weighted average score for this employee. 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?

3.2.2

The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in table #3.2.9 (Lee, 1994).

Table #3.2.9: Lengths of Rivers (km) Flowing to Pacific Ocean

River Length (km) River Length (km)
Clarence 209 Clutha 322
Conway 48 Taieri 288
Waiau 169 Shag 72
Hurunui 138 Kakanui 64
Waipara 64 Waitaki 209
Ashley 97 Waihao 64
Waimakariri 161 Pareora 56
Selwyn 95 Rangitata 121
Rakaia 145 Ophi 80
Ashburton 90

a.) Find the mean and median.

b.) Find the range.

c.) Find the variance and standard deviation.

3.2.6

Print-O-Matic printing company spends specific amounts on fixed costs every month. The costs of those fixed costs are in table #3.2.13.

Table #3.2.13: Fixed Costs for Print-O-Matic Printing Company

Monthly charges Monthly cost ($)
Bank charges 482
Cleaning 2208
Computer expensive 2471
Lease payments 2656
Postage 2117
Uniforms 2600

a.) Find the mean and median.

b.) Find the range.

c.) Find the variance and standard deviation.

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