Exam__1 -Quantitative and Statistical Analysis

Based on the MS Excel file on the Happiness Survey, please see the data in the Excel file and provide the answers to the following (The final submission can either in Excel or in this MS Word file; graphs can be formatted using computer programs or images drawn by hand ):

1. Please list all the variables under two categories: (1) Quantitative variables; (2) Qualitative variables ( 10 points, Review PPT page 5)

Quantitative – age, # of children, education year, # of siblings, income, happiness level (numerical), EQ level (numerical), health level (numerical)

Qualitative – relationship status, marriage status, happiness level, EQ level, health level

2. Please list all the variables under three categories: (1) Nominal; (2) Ordinal; (3) Interval/Ratio (10 Points, Review PPT Page 8).

Nominal – marriage status, relationship status

Ordinal – education year, happiness level, EQ level, health level

Interval/Ratio – age, income, # of children, # of siblings

3. Choose any reasonable variables, please produce (1) one Frequency table; and (2) one Bar/Pie chart (10 Points, Review PPT Page 10 and page 12)

Frequency table

WIDOWED	7
DIVORCED	17
NEVER MARRIED	24
MARRIED	48
SEPARATED	5

Bar chart

4. Choose any reasonable variable, please produce one Histogram graph and write a paragraph of your observations based on the graph (10 Points, Review PPT Page 13; hint: only Interval/Ratio are meaningfully appropriate for histogram )

Frequency distribution (income)

income level	frequency
0 up to 4	3
4 up to 8	1
8 up to 12	8
12 up to 16	17
16 up to 20	36
20 up to 24	30
24 up to 28	6

Histogram (income)

Based on the observations of this histogram, the majority of people fell within the income range of 16 up to 20 (approximately 36%). The second largest concentration of people fell within income range of 20 up to 24 (approximately 30%). The lowest number of people fell within income level range of 4 up to 8 (only 1 person). Median income level is 18.

5. Please choose any reasonable variable and calculate its (1) Mean, (2) Median, (3) Mode, (4) Range (5) and Variance (20 Points, Review PPT Page 15-17; hint: only Interval/Ratio are meaningfully appropriate for such descriptive statistics)

Income

1. mean= 17.29 or 17.3

2. median = 18

3. mode = 18

4. range = 23

5. variance = 4.92

(please see attached excel, tab #5-6)

6. Choose any reasonable variable, please calculate its Standard Deviation and draw a graph for its potential population distribution using the Empirical Rule (10 Points, Review PPT Page 17-18; hint: only Interval/Ratio are meaningfully appropriate for such descriptive statistics)

Income Standard deviation = 4.92 (please see attached excel, tab #5-6)

Mean =17.3

Empirical Rule

7. Choose any reasonable variable, please calculate its quartiles and draw a Box plot (10 Points, Review PPT Page 21-22; hint: only Interval/Ratio are meaningfully appropriate for such descriptive statistics)

Income - quartiles

min	2
Q1	15
Median(Q2)	18
Q3	21
max	25

Box plot

8. Choose any reasonable variable, please draw a Scatter plot and write a paragraph of your observations based on the graph (10 Points, Review PPT Page 24; hint: only Interval/Ratio are meaningfully appropriate for such descriptive statistics)

This scatter plot shows the relationship between a person’s age and the number of children they have. A person’s age is on the horizontal or x-axis, while number of children is displayed on the y-axis. Based on this graph, there appears to be no clear or direct correlation between a person’s ages in relation to how many kids they have. The largest concentration of people ages roughly from 20-70yrs old and have from 0 to 2 kids. Outliers include those with 5 to 6 kids and people near or over the age of 80 who still report having children.

9. Choose any reasonable variable, please draw a Contingency table and write a paragraph of your observations based on the table (10 Points, Review PPT Page 25)

Contingency table showing relationship between happiness level and relationship status

Happiness Level
	Divorced	Married	Never Married	Separated	Widowed	Grand Total
Not too Happy	1	3	7	3	3	17
Pretty Happy	14	26	11	2	4	57
Very Happy	2	19	6			27
Grand Total	17	48	24	5	7	101

Of the total population, approximately 17% are divorced, 48% are married, 24% never married, and the remainder are either separated or widowed. Of those who are divorced, most of them (82%) reported to be “pretty happy”. Less than 1% of those married claim to be unhappy in their marriage. Of those who never married, roughly 71% of them have reported to be happy about their decision. And of those that are either separated or widowed, none of them claimed to be “very happy”. Despite their relationship status, majority of this total population (56%) ultimately reported to be “pretty happy”.

Income

frequency 0 up to 4 4 up to 8 8 up to 12 12 up to 16 16 up to 20 20 up to 24 24 up to 28 3 1 8 17 36 30 6

Number of People

AGE VERSUS NUMBER OF CHILDREN

Children 19 19 19 20 23 24 24 24 24 24 24 27 28 28 29 29 30 31 31 33 33 33 34 35 35 35 35 36 36 36 36 36 37 37 38 38 38 39 40 41 41 41 42 42 43 44 44 44 44 45 46 46 46 46 46 48 49 49 50 50 50 51 51 52 52 53 53 54 54 54 55 55 56 56 56 57 57 59 60 61 61 61 61 63 63 64 64 64 65 65 65 65 66 66 67 68 68 69 79 82 82 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 4 2 2 2 4 3 3 4 6 1 2 0 3 2 0 0 0 0 0 2 3 2 1 4 0 2 4 3 3 2 3 2 1 3 2 1 2 2 3 1 2 2 0 5 2 2 2 3 0 2 4 3 0 6 2 0 0 0 2 3 3 0 4 2 3 3 3 1 0 3 3 2 2 2 2 2 5 4 3 3 3

AGE

# OF CHILDREN

WIDOWED DIVORCED NEVER MARRIED MARRIED SEPARATED 7 17 24 48 5