STAT 200 Assignment 3
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Assignment21.rtfSTAT200: Assignment #2 - Descriptive Statistics Analysis Writeup - Template
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University of Maryland University College
STAT200 - Assignment #2: Descriptive Statistics Analysis and Writeup
Identifying Information
Student (Full Name):
Class: STAT 200
Instructor:
Date:
Introduction:
Descriptive statistics are used to describe the basic features of data in a study. We use descriptive statistics to describe the data. With graphics analysis, they form a baseline quantitative analysis of data. Descriptive statistical measures is an effective ways to properly define these statistical attributes.
Scenario: I am the head of household as a single parent and only source of income. I have obtained a high school diploma for education. I have one child that I am the sole provider for.
Table 1. Variables Selected for the Analysis
Variable Name in data set
Description
Type of Variable (Qualitative or Quantitative)
Variable 1: “Income”
Annual household income in USD.
Quantitative
Variable 2: “Marital Status”
Marital Status as the Head of Household
Qualitative
Variable 3: “Family Size”
Total number of people in the house to include adults and children
Quantitative
Variable 4: “Annual Expenditures”
Total amount of annual expenditures
Quantitative
Variable 5: “Age Head of Household”
Age of Head of Household
Quantitative
Data Set Description and Method Used for Analysis :
The provided data on comparison among attributes of the data which is picked by random sample from the US Department of Labor’s 2016 Consumer Expenditure Surveys (CE) and provides information about the composition of households and their annual expenditures. It contains information from 30 households, where a survey provided the requested information; it is all self-reported information. This dataset contains five socioeconomic variables (whose names start with SE) and four expenditure variables (whose names start with USD). By analyzing and examining data, we can make and draw logical conclusions based on the result of the descriptive statistics.
Results:
The result of the descriptive statistics of the picked variables are:
Table 2. Descriptive statistics
SE-incomeSE-AgeHeadHouseholdSE-FamilySizeUSD-AnnualExpenditures
Mean99535.9744.173.1066165.53
Standard Error1007.182.000.241989.47
Median9690744363142.5
Mode#N/A592#N/A
Standard Deviation5516.5710.951.3210896.76
Sample Variance30432541.83119.871.75118739296.53
Kurtosis1.52-0.46-0.67-1.71
Skewness1.65-0.490.480.26
Range1918442529557
Minimum9486718154929
Maximum11405160684486
Sum29860791325931984966
Count30303030
SE-income
SE-AgeHeadHousehold
SE-FamilySize
USD-AnnualExpenditures
Mean
99535.97
44.17
3.10
66165.53
Standard Error
1007.18
2.00
0.24
1989.47
Median
96907
44
3
63142.5
Mode
#N/A
59
2
#N/A
Standard Deviation
5516.57
10.95
1.32
10896.76
Sample Variance
30432541.83
119.87
1.75
118739296.53
Kurtosis
1.52
-0.46
-0.67
-1.71
Skewness
1.65
-0.49
0.48
0.26
Range
19184
42
5
29557
Minimum
94867
18
1
54929
Maximum
114051
60
6
84486
Sum
2986079
1325
93
1984966
Count
30
30
30
30
Numerical Summary :
Measure(s) of Central Tendency for the quantitative variables I have picked in my analysis:
Table 3. Measure(s) of Central Tendency
NameCount (n)MeanMedianMode
Variable 1
SE-income3099535.9796907#N/A
Variable 2
SE-AgeHeadHousehold3044.174459
Variable 4
SE-FamilySize303.1032
Variable 4
USD-AnnualExpenditures3066165.5363142.5#N/A
Measure(s) of Central Tendency
Name
Count (n)
Mean
Median
Mode
Variable 1
SE-income
30
99535.97
96907
#N/A
Variable 2
SE-AgeHeadHousehold
30
44.17
44
59
Variable 4
SE-FamilySize
30
3.10
3
2
Variable 4
USD-AnnualExpenditures
30
66165.53
63142.5
#N/A
Measure(s) of Central Tendency
Measure(s) of Dispersion for the quantitative variables I have picked in my analysis:
Table 4. Measure(s) of Dispersion
Name
Sample VarianceStandard Deviation1st Quartile3rd QuartileRangeIQR
Variable 1SE-income30432541.835516.5796534.5100511.251918481327.25
Variable 2SE-AgeHeadHousehold119.8710.9537.552.754210.75
Variable 4SE-FamilySize1.751.32245-1
Variable 4USD-AnnualExpenditures118739296.5310896.7655939.7574492.52955744935.5
Measure(s) of Dispersion
Name
Sample Variance
Standard Deviation
1st Quartile
3rd Quartile
Range
IQR
Variable 1
SE-income
30432541.83
5516.57
96534.5
100511.25
19184
81327.25
Variable 2
SE-AgeHeadHousehold
119.87
10.95
37.5
52.75
42
10.75
Variable 4
SE-FamilySize
1.75
1.32
2
4
5
-1
Variable 4
USD-AnnualExpenditures
118739296.53
10896.76
55939.75
74492.5
29557
44935.5
Measure(s) of Dispersion
Result Interpretation
A measure of central tendency (also referred to as measures of center or central location) is a summary that describes a set of data with a single value that represents the middle or center of its distribution.
There are three main measures of central tendency: the mode, the median and the mean.
The mean value for all selected variables in this analysis are:
SE-Income is 99535.97, SE-AgeHeadHousehold is 44.17, and USD-Annual Expenditures is 66165.53.
The median value for all selected variables in this analysis are
SE-Income is 96907, SE-AgeHeadHousehold is 44.00, USD-Annual Expenditures is 63142.5. The mode value for all selected variables in this analysis are
SE-AgeHeadHousehold is 59.00, and no mode value for SE-Income, USD-Annual Expenditures.
The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical.
In the analysis variable SE-Income is high so for these variables the median is preferred central tendency.
From the table 4 we conclude that the variation around the mean of the variables SE-Income, USD-AnnualExpenditures are very high.
Graph and/or Table: Histogram of Income
BIN
Frequency
98867
21
102867
3
106867
2
110867
1
114867
3
Description of Findings.
For most of the people income is in between 94867 and 98867. The data is skewed to the right.
Graph and/or Table. : SE-AgeHeadHousehold
BIN
Frequency
28
2
38
6
48
9
58
10
68
3
Description of Findings.
The age of the people is in between 48 and 58. The data is almost normal distributed
Variable 3: ( SE-FamilySize )
Graph and/or Table.
BIN
Frequency
2
12
3
8
4
4
5
5
6
1
The size of the maximum families is 1 to 3. The data is skewed to the right.
Variable 4: ( USD-AnnualExpenditures )
Graph and/or Table.
BIN
Frequency
60929
15
66929
0
72929
2
78929
8
84929
5
Variable 5: (SE-MaritalStatus)
MarriedNot MarriedTotal
151530
SE-MaritalStatus
Variable 5
Married
Not Married
Total
15
15
30
SE-MaritalStatus
Variable 5
The pie chart that there is exactly 50% married and 50% unmarried in the sample data set.
Description of Findings .
For most of the Annual Expenditures is between 54929 and 60929. There is no pattern in the data
Conclusion:
The mean is influenced by outliers and skewed distributions then we preferred median central of tendency. The mode has an advantage over the median and the mean as it can be found for both numerical and category.
