Question

In: Statistics and Probability

5. What is the skewness and kurtosis of each data set? 6. Generate a histogram plot...

5. What is the skewness and kurtosis of each data set? 6. Generate a histogram plot of each of the data sets. 7. Based on the variability of the data, what do you think the next step would be to analyze the data? Age Income 29 9315 25 6590 28 9668 27 8412 25 1654 24 2431 25 6977 19 8966 27 9327 18 3871 25 9934 19 2236 19 3035 29 2518 19 3616 19 9219 28 1090 18 5368 26 2832 29 1899

Solutions

Expert Solution

5. The summary statistics for each data-set is as follows;

Age
Mean 23.9
Standard Error 0.9316086822
Median 25
Mode 19
Standard Deviation 4.166280684
Sample Variance 17.35789474
Kurtosis -1.5946043
Skewness -0.3145955467
Range 11
Minimum 18
Maximum 29
Sum 478
Count 20
Income
Mean 5447.9
Standard Error 724.4938411
Median 4619.5
Mode 9934
Standard Deviation 3240.034956
Sample Variance 10497826.52
Kurtosis -1.769589839
Skewness 0.1720874245
Range 8844
Minimum 1090
Maximum 9934
Sum 108958
Count 20

From the above tables we observe the value of skewness and kurtosis.

The same has been calculated using the Data analysis option in MS Excel.

6. Histogram for Age:

Bin Frequency Cumulative %
18 2 10.00%
20 5 35.00%
22 0 35.00%
24 1 40.00%
26 5 65.00%
28 4 85.00%
30 3 100.00%
More 0 100.00%

Histogram for Income:

Bin Frequency Cumulative %
2000 3 15.00%
4000 7 50.00%
6000 1 55.00%
8000 2 65.00%
10000 7 100.00%
More 0 100.00%

7. Based on the data our next step would be to calculate the correlation between age and income.

Age Income
Age 1
Income 0.06171967151 1

We observe a very low correlation between age and income. The value is 0.06.


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