Question

choose a data that research interests, taking into consideration that the data consists qualitative and quantitative variables. (using the available data sources, i.e. questionnaire, records, approved electronic sites, ....etc.)

please solve it clearly and make sure it's correct 100%

Answer 1

Greetings of the day!

Answer:

A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.

Quantitative Variables - Variables whose values result from counting or measuring something.

Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper

Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.

Examples: hair color, religion, political party, profession

Designator - Values that are used to identify individuals in a table. Designator values usually do not repeat in a table, but variable values often do repeat.

Qualitative Methods	Quantitative Methods
Methods include focus groups, in-depth interviews, and reviews of documents for types of themes	Surveys, structured interviews & observations, and reviews of records or documents for numeric information
Primarily inductive process used to formulate theory or hypotheses	Primarily deductive process used to test pre-specified concepts, constructs, and hypotheses that make up a theory
More subjective: describes a problem or condition from the point of view of those experiencing it	More objective: provides observed effects (interpreted by researchers) of a program on a problem or condition
Text-based	Number-based
More in-depth information on a few cases	Less in-depth but more breadth of information across a large number of cases
Unstructured or semi-structured response options	Fixed response options
No statistical tests	Statistical tests are used for analysis
Can be valid and reliable: largely depends on skill and rigor of the researcher	Can be valid and reliable: largely depends on the measurement device or instrument used
Time expenditure lighter on the planning end and heavier during the analysis phase	Time expenditure heavier on the planning phase and lighter on the analysis phase
Less generalizable	More generalizable

Examples: name, rank, jersey number of a team member, cell phone number, license number.

It is important to identify whether the data are quantitative or qualitative as this affects the statistics that can be produced.


Frequency counts:

The number of times an observation occurs (frequency) for a data item (variable) can be shown for both quantitative and qualitative data.

The graphs below arrange the quantitative and qualitative data to show the frequency distribution of the data.


Quantitative Data




Qualitative Data



As absolute frequencies can be calculated on quantitative and qualitative data, relative frequencies can also be produced, such as percentages, proportions, rates and ratios. For example, the graphs above show 4 people (20%) worked less than 30 hours per week, and 6 people (30%) are teachers.


Descriptive (summary) statistics:

Statistics that describe or summarise can be produced for quantitative data and to a lesser extent for qualitative data.

As quantitative data are always numeric they can be ordered, added together, and the frequency of an observation can be counted. Therefore, all descriptive statistics can be calculated using quantitative data.

As qualitative data represent individual (mutually exclusive) categories, the descriptive statistics that can be calculated are limited, as many of these techniques require numeric values which can be logically ordered from lowest to highest and which express a count.

Mode can be calculated, as it it the most frequency observed value. Median, measures of shape, measures of spread such as the range and interquartile range require an ordered data set with a logical low-end value and high-end value. Variance and standard deviation require the mean to be calculated, which is not appropriate for categorical variables as they have no numerical value.


Inferential statistics:

By making inferences about quantitative data from a sample, estimates or projections for the total population can be produced.

Quantitative data can be used to inform broader understandings of a population, or to consider how that population may change or progress into the future.

For example, a simple income projection for an employee in 2015 may be inferred from the rate of change for data collected in 2000, 2005, and 2010.

As shown in the graph below, data collected over time indicates a 5% increase every five years. Therefore, if the rate of increase continues to follow the same pattern, it can be projected that the annual income for that employee in 2015 will be $46,305; which is the 2010 wage of $44,100 increased by an additional 5%.




Qualitative data are not compatible with inferential statistics as all techniques are based on numeric values.

Exercises: In the tables below identify which columns represent qualitative variables, which columns represent quantitative variables, and which columns represent designators.

1) Highest U.S. Dams

Name	Height	River	State	Completed
Oroville	754	Feather	CA	1968
Hoover	725	Colorado	NV	1936
Dworshak	718	N Fork Clearwater	ID	1873
Glen Canyon	708	Colorado	AZ	1966
New Bullards Bar	636	North Yuba	CA	1970
New Melones	626	Stanislaus	CA	1979
Swift	610	Lewis	WA	1958
Mossyrock	607	Cowlitz	WA	1968
Shasta	600	Sacramento	CA	1945
Hungry Horse	564	S Fork Flathead	MT	1953
Grand Coulee	551	Columbia	WA	1942
Ross	541	Skagit	WA	1949

Source: The World Almanac and Book of Facts 1998

2) Super Bowls

No.	Year	Winner	Winning Score	Loser	Losing Score	Winning Coach	Game Site
I	1967	Packers	35	Chiefs	10	Lombardi	Los Angeles
II	1968	Packers	33	Raiders	14	Lombardi	Miami
III	1969	Jets	16	Colts	7	Ewbank	Miami
IV	1970	Chiefs	23	Vikings	7	Stram	New Orleans
V	1971	Colts	16	Cowboys	13	McCafferty	Miami
VI	1972	Cowboys	24	Dolphins	3	Landry	New Orleans
VII	1973	Dolphins	14	Redskins	7	Shula	Los Angeles
VIII	1974	Dolphins	24	Vikings	7	Shula	Houston
IX	1975	Steelers	16	Vikings	6	Noll	Miami
X	1976	Steelers	21	Cowboys	17	Noll	Pasadena
XI	1977	Raiders	32	Vikings	14	Madden	New Orleans

Source: The World Almanac and Book of Facts 1998

ANSWER:

Accuracy and Scientific Notation

1) 0 places, 3 sig. digits, 5.42 x 104	2) 0 places, 5 sig. digits, 1.7846 x 108
3) 7 places, 4 sig. digits, 2.314 x 10-4	4) 5 places, 3 sig. digits, 9.80 x 10-3
5) 3 places, 6 sig. digits, 1.32502 x 102	6) 2 places, 4 sig. digits, 3.741 x 101
7) 4 places, 4 sig. digits, 3.473 x 10-1	8) 1 place, 5 sig. digits, 1.4453 x 103
9) 4.897	10) 245.12	11) 83.1	12) 0.432
13) 110	14) 27.34	15) 539,500	16) 4,390,000
17) 0.00435	18) 0.0006288	19) 57,789	20) 312,200
21) 0.008324	22) 0.0000769

Comparing Modified Boxplots

1)	8 AM is more skewed, 9 AM has largest value, 9 AM has smallest value, 8 AM has largest median, 9 AM has largest range, 9 AM has largest IQR
2)	11 AM is more skewed, 10 AM has largest value, 11 AM has smallest value, 10 AM has largest median, the ranges are the same and 11 AM has largest IQR.
3)	1 PM is more skewed, the largest values are about the same, 2 PM has the smallest value, 1 PM has largest median, 2 PM has the largest range and largest IQR.
4)	3 PM is more skewed, 3 PM has largest value, 4 PM has smallest value, 3 PM has largest median, 4 PM has the largest range and IQR.
5)	5 PM is more skewed, 5 PM has largest value, 6 PM has smallest value, 5 PM has largest median, 5 PM has the largest range, the IQR's are about the same.

Computing Formula Values

1) 74.08	2) 55.73	3) 0.4733	4) 0.1475
5) 2.72	6) -0.85	7) -0.7171	8) 0.7191
9) 1,637,000	10) 265,400	11) 295.6	12) 94.88

Coefficients of Determination and Correlation

1) 45.2% of the variation is explained by the regression line.
2) 91.3% of the variation is explained by the regression line.
3) 72.1% of the variation is explained by the regression line.
4) 26.4% of the variation is explained by the regression line.
5) weak positive correlation	6) no correlation
7) strong positive correlation	8) perfect negative correlation
9) moderate positive correlation	10) moderate negative correlation
11) no correlation	12) strong negative correlation

Grouped Data

1) mean = 32.2, std. dev. = 11.1	2) mean = 10.7, std. dev. = 9.6
3) mean = 15.6, std. dev. = 10.8	4) mean = 21.1, std. dev. = 11.7
5) mean = 44.0, std. dev. = 10.6	6) mean = 80.5, std. dev. = 8.1
7) mean = 36.8, std. dev. = 7.6	8) mean = 31.6, std. dev. = 5.2

Histogram Analysis

1)	minimum = 18, maximum = 60, skewed left, one peak at 45,one gap between 24 and 30, no extreme values
2)	minimum = 12, maximum = 108, skewed left, two peaks at 54 and 90, one gap between 24 and 36, no extreme values
3)	minimum = 0, maximum = 500, skewed right, one peak at 25, 3 gaps: between 100 and 150, between 200 and 250, and between 300 and 400. Since the last gap is twice as large, values between 400 and 500 are extreme.
4)	minimum = 15, maximum = 40, skewed right, two peaks at 27.5 and 37.5 (but the second peak is barely a peak), no gaps or extreme values.

Outliers and Influential Observations

1) outlier near (12.9, 24.4), influential observation near (9.9, 16.1)

2) outlier near (112, 86), influential observation near (129, 121)

3) outlier near (53, 88), influential observations near (68, 108) and (76, 111)

Parameters and Statistics

1)	The parameter is the average height of all women aged 20 years or older.
The statistic is the average height of 63.9 inches from the sample of 45 women.
2)	The parameter is the mean amount of sodium consumed by children under the age of ten.
The statistic is the mean of 2993 milligrams of sodium obtained from the sample of 75 children.
3)	The parameter is the proportion of patients healed by Nexium in 8 weeks.
The statistic is 213/224 = 0.951, the proportion healed in the sample.
4)	The parameter is the average farm size in Kansas.
The statistic is the mean farm size of 731 acres from the sample of 40 farms.
5)	The parameter is the average oil output per well in the United States.
	The statistic is the mean oil output of 10.7 barrels per day from the sample of 50 wells.
6)	The parameter is the proportion of adults 18 or older who read a book in the previous year.
	The statistic is 835/1006 = 0.830, the proportion who read a book in the sample.
7)	The parameter is the average amount of calcium that male teenagers consume.
	The statistic is the mean of 1081 milligrams of calcium from the sample of 50 teenagers.
8)	The parameter is the proportion of adults with kids under 18 who ate together 7 days a week.
	The statistic is 337/1122 = 0.300, the proportion in the sample who ate together.
9)	The parameter is the mean verbal SAT score for students whose first language is not English.
	The statistic is the mean SAT verbal score of 458 from the sample of 20 students.

Qualitative vs. Quantitative

1)

Name - designator, Height - quantitative, River - qualitative, State - qualitative, Completed - quantitative

2)

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