STAT 200 Week 2

Problem 1. The median incomes of females in each state of the United States, including the District of Columbia and Puerto Rico, are given in the table below.

Table: 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

(a) Create a frequency distribution, relative frequency distribution, and cumulative frequency distribution for the data in the table distribution using 7 classes.

(b) Create a frequency histogram and relative frequency histogram for the data in the table. Based on the histograms, describe the shape of the distribution.

(c) Create an ogive for the data in the table.

(d) Describe any findings you can from the graphs in (b) and (c).

Problem 2. The table below contains the value of houses and the amount of rental income in a year that each of these houses brings in.

Table: 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

Create a scatter plot of the data above and determine if there is a linear (positive or negative) relationship (or no linear relationship) between the value of the house and its annual rental income.

Problem 3. 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 2006 through March 2013 are contained in the table below.

Table: 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

Create a time-series plot of the data in the above table and interpret any findings.

Problem 4. The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in the table below.

Table: Length of Rivers (km) Flowing to the Pacific Ocean

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

For the data in the above table, find the following:

(a) Mean

(b) Median

(c) Mode

(d) Range

(e) Variance

(f) Standard Deviation

Problem 5. State which type of measurement scale (e.g., nominal, ordinal, etc.) each of the following represents, and then which center measures (e.g., mean, mode, etc.) can be used for the variable?

(a) You collect data on the height of plants using a new type of soil.

(b) You collect data on the cars that people drive in Sydney, 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 wine competition.

Problem 6. Employees at Anne Arundel Community College (AACC) are evaluated based on goal setting and accomplishments toward goals, job effectiveness, competencies, and AACC 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 weight of 4%

Competency 2 has a weight of 3%

Competency 3 has a weight of 3%

Competency 4 has a weight of 5%

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.

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

(b) AACC policy is that if an employee has a weighted average score less than 2.5, the employee must have a Performance Enhancement Plan written.Does this employee need a plan?

Problem 7.The We-Print-Everything printing company spends specific amounts on fixed costs every month. The fixed costs are shown in the table below.

Table: Fixed Costs for the We-Print-Everything Printing Company

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

For the data in the above table, find the following:

(a) Mean

(b) Median

(c) Range

(d) Variance

(e) Standard Deviation