University of Maryland University College

University of Maryland University College

STAT200 – Assignment #2: Descriptive Statistics Analysis and Writeup

Identifying Information

Class: STAT 200 6373 Introduction to Statistics (2202)

Date: 5^th February 2020

Introduction:

Scenario: I am 45 years old, married, and the head of a household. I have a degree in Business Management. I have two children. I earn $101,829 and spend $10,821 on food, and $810 on education.[unique_solution]

Table 1. Variables Selected for the Analysis

Data Set Description and Method Used for Analysis:

Results:

Variable 1: Income

This variable is crucial in catering for the necessities required by the family to survive.

Numerical Summary.

Income analysis quantitatively through a measure of central tendency to get the median, and Mean. Mean is usually important when the sample is uniformly distributed. However, the median will be preferred measure of central tendency when data is not normally distributed due to outliers.

The sample standard deviation was the measure of dispersion because the data represents a sample of data set.

A histogram was used to show the normal distribution of data.

Table 2. Descriptive Analysis for Variable 1

Graph and/or Table: Histogram of Income

Description of Findings.

It is skewed to the right, which implies that the number of people earning high-income decreases as the level of income increases. Most people are earning less than the mean income ($99661.03).  The dispersion level is not as high as the Standard Deviation of $5138.966 was not high. These imply most people earn averagely with the only difference of about $5138.966

Variable 2: Age Head Household

Numerical Summary.

Median, mode, and mean were used as a measure of central tendency because the variable is quantitative.

The sample standard deviation was the measure of dispersion.

A histogram was used to show the normal distribution of Age Head data.

Table 3. Descriptive Analysis for Variable 2

Graph and/or Table.

Description of Findings.

The histogram is skewed towards the left, which implies that more people are old.  Most are over 40 years. The mean is 47.03333 years, whereas the median was 50 years. More than one person had 51 years based on the mode. Most of the sampled people had commonalities in age. On the other hand, the SD of 8.479116 means that ages among the respondents differed with about 8 years compared to the sample mean.

Variable 3: Family Size

The family size is another significant variable expenses.

Numerical Summary.

Median, mode, and mean were used as a measure of central tendency because the variable is quantitative.

The sample standard deviation was the measure of dispersion.

Pie Chart was preferred in this case to compare the distribution based on the number of family members in each category.

Table 4. Descriptive Analysis for Variable 3

Graph and/or Table.

Description of Findings.

There was consistency in the family sizes as the Mean was 2.833333, Median at 3, whereas the Mode was 3. It shows that average families have 3 people. However, based on the mode, most have 3 followed by 2 people at 36 and 33%, respectively. The Pie chart reveals that about 70% have either 2 or 3 individuals. On the other hand, there was little deviation from mean given the SD= 1.019917, which can be interpreted as most families slightly more or less as 3 children.

Variable 4: Food Expenditures

Food expenditure is another important variable because the amount of money that is spent on food will entirely be depending on the income and the size of the household. After all, food is the one basic necessity for survival.

Numerical Summary.

Median and mean were used as a measure of central tendency because the variable is quantitative.

The sample standard deviation was the measure of dispersion.

A histogram was used to show the normal distribution of Food Expenditure data.

Table 5. Descriptive Analysis for Variable 4

Graph and/or Table.

Description of Findings.

Based on the histogram, it is evident that the distribution of food expenditures have an almost similar trend as the income levels. Most people are spending less than the Mean of 8504.867. Only a few can manage to spend more than the average expenditures. Based on the SD of 1646.068, the deviation from the mean food expenditures is not high.

Variable 5: Education Expenditures

Numerical Summary.

Median and mean were used as a measure of central tendency because the variable is quantitative.

The sample standard deviation was the measure of dispersion.

A histogram was used to show the normal distribution of Education Expenditures data.

Table 6. Descriptive Analysis for Variable 5

Graph and/or Table.

Description of Findings.

The distribution is bell-shaped, which means that most people spend averagely 348.3 with only a few spending more or less on education. The dispersion is equally noticeable based on the SD of 187.4512. It shows a sizeable difference from the mean expenditure on education.

Discussion and Conclusion.

Based on the line graph above, most of the expenditures are on food whereas less is spent on entertainment. However, there is some respondent who spent more on entertainment than on food. The highest expenditure on Education, food, and Entertainment was $810, $11375, and $201, respectively. On the other hand, the lowest expenditures of the above components were $11, $6822, and $38. Therefore, the respondents should save more on entertainment to ensure there is enough money to cater for food and education.  Some people have emphasized more on entertainment yet spend less on education. If more is spent on education, it will boost the chances of earning more income.