a. Is the histogram symmetric? Is the histogram bell-shaped? b. Can you apply th

Question

a. Is the histogram symmetric? Is the histogram bell-shaped?

b. Can you apply the empirical rule (the 68-95-99.7 rule) to this data set? Why or why not?

Salary / Data Set #1 Histogram Bin Min Bin Max Bin Midpoint Freq. Rel. Freq. Prb. Density Bin #1 $33077.00 $39855.80 $36466.40 17 0.0850 0.000013 Bin #2 $39855.80 $46634.60 $43245.20 42 0.2100 0.000031 Bin #3 $46634.60 $53413.40 $50024.00 38 0.1900 0.000028 Bin #4 $53413.40 $60192.20 $56802.80 3 0.0150 0.000002 Bin #5 $60192.20 $66971.00 $63581.60 0 0.0000 0.000000 Bin #6 $66971.00 $73749.80 $70360.40 1 0.0050 0.000001 Bin #7 $73749.80 $80528.60 $77139.20 21 0.1050 0.000015 Bin #8 $80528.60 $87307.40 $83918.00 46 0.2300 0.000034 Bin #9 $87307.40 $94086.20 $90696.80 29 0.1450 0.000021 Bin #10 $94086.20 $100865.00 $97475.60 3 0.0150 0.000002 Histogram of Salary / Data Set #1 50 46 45 42 38 29 30 5 25 21 15 10

Explanation / Answer

a) Yes, the histogram is symmetric but is is not bell shaped because it is a bimodal histogram. For it to be a bell shaped histogram, the frequencies should start from minimum, goes to highest and then again drops to minimum which is not the case here.

b) Since the salaries aren't bell shaped i.e. they aren't normally distributed, we can't use 68-95-99.7 rule in this data set.

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