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

  • 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

  • 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

WIDOWED7
DIVORCED17
NEVER MARRIED24
MARRIED48
SEPARATED5

Bar chart

  • 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 levelfrequency
0 up to 43
4 up to 81
8 up to 128
12 up to 1617
16 up to 2036
20 up to 2430
24 up to 286

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.

  • 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
    1. median = 18
    1. mode = 18
    1. range = 23
    1. variance = 4.92

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

  • 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

  • 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

min2
Q115
Median(Q2)18
Q321
max25

Box plot

  • 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.

  • 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
DivorcedMarriedNever MarriedSeparatedWidowedGrand Total
Not too Happy1373317
Pretty Happy1426112457
Very Happy219627
Grand Total17482457101

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”.

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