Statistics for Business and Finance Examining Household data

Statistics for Business and Finance
Assignment 1 – Examining Household data
Phuc Thang Nguyen
Student number: 20170603
1

Task 1: Preparing data for analysis
Task 2: Describing data
A.
ATaxInc Texp Meals Cloth
Mean AUD 63,409.96 AUD 25,367.54 AUD 1,064.14 AUD 1,007.49
Standard Error AUD 3,145.37 AUD 2,234.51 AUD 66.53 AUD 131.49
Median AUD 54,010.50 AUD 20,847.00 AUD 720.00 AUD 600.00
Mode AUD 36,043.00 AUD 14,998.00 AUD 0.00 AUD 600.00
Standard
Deviation AUD 49,732.66 AUD 35,330.75 AUD 1,051.99 AUD 2,079.07
Sample
Variance
AUD
2,473,337,411.89
AUD
1,248,261,749.31
AUD
1,106,686.53
AUD
4,322,542.23
Kurtosis AUD 20.45 AUD 189.59 AUD 4.89 AUD 159.53
Skewness AUD 3.51 AUD 12.95 AUD 1.92 AUD 11.49
Range AUD 410,040.00 AUD 542,646.00 AUD 6,000.00 AUD 30,300.00
Minimum AUD 8,450.00 AUD 2,303.00 AUD 0.00 AUD 0.00
Maximum AUD 418,490.00 AUD 544,949.00 AUD 6,000.00 AUD 30,300.00
Sum AUD 15,852,489.00 AUD 6,341,886.00
AUD
266,036.00 AUD 251,872.00
Count AUD 250.00 AUD 250.00 AUD 250.00 AUD 250.00
25th percentile AUD 31,565.25 AUD 15,006.75 AUD 360.00 AUD 240.00
75th percentile AUD 80,763.00 AUD 29,503.25 AUD 1,440.00 AUD 1,200.00
Interquartile AUD 49,197.75 AUD 14,496.50 AUD 1,080.00 AUD 960.00
25th percentile: = quartile (data range, 1)
75th percentile = quartile (data range, 3)
Interquartile = 75th percentile – 25th percentile
B.
Location parameter determines the location of a distribution. Location parameter is consisted of
mean, median, and mode. (Thomas, 2015). Mean is the arithmetic average value of a data set.
Median is the midpoint of a data set which half of observations lies above and below. Mode is
the most frequent number in the data set (Michael, 2013).
Spread of a data set is illustrated by standard deviation and variance. Standard deviation is square
root of variance. They measure how far numbers from their means.
Skewness measures how asymmetry of a distribution. (James and Mark, 2008). A normal
distribution has skewness of 0.
2

Kurtosis states how peaked and tail’s mass of a distribution from a normal one. James and Mark
(2008, p.25) states that “the greater the kurtosis of a distribution, the more likely are outliers”.
Kurtosis of a normal distribution equals three.
C.
Mean of “ATaxInc” is the highest at AUD 63,409.96, indicating net average household income
per year at AUD 63,409.96. This figure is higher 2.5-time than total average household
expenditures per year (around AUD 25,367.54). Average annual meals expenditure (AUD
1,064.14) is higher than average annual clothing expenditures (AUD 1,007.49), meaning people
pay more for meals.
Median of “ATaxInc” represents the center of net household income per year in Australia at
AUD 54,010.50. This is much greater than median of “Texp”, which is total household
expenditures yearly. Median of “Meals” and “Cloth” is relatively equally.
Mode of “ATaxInc” is at AUD 36,043.00, indicating many people earns net annual income at
AUD 36,043.00. It is noted that mode of “Meals” is zero, meaning many people did not spend
meals eaten out.
D.
E.
Net household income per year of Australians concentrates on the lower range from AUD35,786
to AUD117,794. As a result, distribution of “ATaxInc” is negatively skewed.
The majority of total household expenses yearly of Australians lies in AUD38,479.4.
3
8450.00
63122.00
117794.00
172466.00
227138.00
281810.00
336482.00
391154.00
0
40
80
Histogram of ATaxInc
Frequency
Bin
Frequency
2303.00
74655.80
147008.60
219361.40
291714.20
364067.00
436419.80
508772.60
0
100
200
Histogram of Texp
Frequency
Bin
Frequency