Bureau of Labor Statistic on Consumer Spending. The BLS tracks consumer spending
ID: 3041236 • Letter: B
Question
Bureau of Labor Statistic on Consumer Spending. The BLS tracks consumer spending every quarter (i.e., Jan – March) using a representative random sample of 4,200 Americans who report themselves as “head of household” on their taxes. This data is from Q1 of 2015. The table below displays a 5-number summary of the samples.
Total Expenditures
Food Expenditures
Housing Expenditures
Entertainment Expenditures
Annual Salary
(your choice, type name)
Min
0.00019
0
0
0
0
-1650
Q1
0.24696
433.3
899
51
0
16
Median
0.50047
751.7
1545
130
34621
263.3
Q3
0.75436
1252
2660
270
76000
666.7
Max
1
7886.7
121432
12960
441675
17795.8
Mean
0.50042
962.4
2132
256.7
52479
530.6
St. Deviation
0.29107
783.9
2783
533.9
63396
876
Skewness
-0.00
2.26
20.63
11.19
2
5.59
- When discussing data on “typical” total monthly expenditures per household, should the BLS report means or medians? Why?
- What amount of quarterly housing expenditures would qualify as a high outlier? In other word, what is the “high outlier” cut-off, knowing that an outlier is 1.5IQR’s above Q3. How many households out of the 4,200 are outliers on quarterly housing spending? Finally, in your opinion, should the BLS keep these outliers in their analyses or drop them, and why?
-Let’s say we want to know what annual salary cuts off the top 10% and 1% of earners from the rest. Using the mean and standard deviation for “Annual Salary” as well as your knowledge of z-scores, tell me what someone’s salary needs to be to be in the top 10%? What about the top 1%
Total Expenditures
Food Expenditures
Housing Expenditures
Entertainment Expenditures
Annual Salary
(your choice, type name)
Min
0.00019
0
0
0
0
-1650
Q1
0.24696
433.3
899
51
0
16
Median
0.50047
751.7
1545
130
34621
263.3
Q3
0.75436
1252
2660
270
76000
666.7
Max
1
7886.7
121432
12960
441675
17795.8
Mean
0.50042
962.4
2132
256.7
52479
530.6
St. Deviation
0.29107
783.9
2783
533.9
63396
876
Skewness
-0.00
2.26
20.63
11.19
2
5.59
Explanation / Answer
Ques
- When discussing data on “typical” total monthly expenditures per household, should the BLS report means or medians? Why?
Ans:
IQR = Q3 – Q1 = 0.5074
Lower Bound = Q1 – 1.5 * IQR = -0.5414
Upper Bound = Q3 + 1.5 * IQR = 1.5154
Since the min and max values are inside the interval (Lower Bound, Upper Bound), so there are no outliers. Hence, we should use Mean for “typical” total monthly expenditures.
Ques:
- What amount of quarterly housing expenditures would qualify as a high outlier? In other word, what is the “high outlier” cut-off, knowing that an outlier is 1.5IQR’s above Q3. How many households out of the 4,200 are outliers on quarterly housing spending? Finally, in your opinion, should the BLS keep these outliers in their analyses or drop them, and why?
Ans:
For housing expenditures,
IQR = Q3 – Q1 = 1761
Lower Bound = Q1 – 1.5 * IQR = -1742.5
Upper Bound = Q3 + 1.5 * IQR = 5301.5
High Outlier cut-off = upper bound = 5301.5.
Any value above this value is an outlier.
Since the data of 4,200 is not given, it is not possible to give exact number of outliers.
The decision to either drop or keep the outliers depends on the type of Study BLS is conducting.
If they are interested in the average household needs, then they should drop these outliers.
However, if they are interested in the behaviour of the extreme values, they should not drop the outliers.
Ques:
-Let’s say we want to know what annual salary cuts off the top 10% and 1% of earners from the rest. Using the mean and standard deviation for “Annual Salary” as well as your knowledge of z-scores, tell me what someone’s salary needs to be to be in the top 10%? What about the top 1%
Ans:
We will caculate the Z-value of Botton 10% from the Z-table and ie value of Z where probability is .1
This is Z = -1.28
So, for top 10%,
Z = 1.28
Now we will use the formulae,
Z = (x-Mean)/std Dev, ie X = Mean + Z * Std Dev
For Annual Salary,
Mean = 52479
Std Dev = 63396
Hence X = 133625.88. All Salary above this value constitute the Top 10%.
Similarly, for Top 1%
Z = 2.33
Hence, X = 200191.68
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