Question

The frequency distribution was obtained using a class width of 0.5 for data on cigarette tax...

The frequency distribution was obtained using a class width of 0.5 for data on cigarette tax rates. Use the frequency distribution to approximate the population mean and population standard deviation. Compare these results to the actual mean mu equals=​$1.635 and standard deviation sigma equals=​$1.104.

1. What is population mean

2. What is standard deviation

Data:

Tax Rate Lower Limit Upper Limit Frequency
0.00-0.49 0 0.49 5
0.50-0.99 0.5 0.99 13
1.00-1.49 1 1.49 6
1.50-1.99 1.5 1.99 6
2.00-2.49 2 2.49 5
2.50-2.99 2.5 2.99 5
3.00-3.49 3 3.49 3
3.50-3.99 3.5 3.99 1
4.00-4.49 4 4.49 2
Math   Statistics-And-Probability   
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Homework Answers

Answer #1
Class interval Midpoint, x Frequency, f fx fx²
0 - 0.49 0.245 5 1.225 0.300125
0.5 - 0.99 0.745 13 9.685 7.215325
1 - 1.49 1.245 6 7.47 9.30015
1.5 - 1.99 1.745 6 10.47 18.27015
2 - 2.49 2.245 5 11.225 25.200125
2.5 - 2.99 2.745 5 13.725 37.675125
3 - 3.49 3.245 3 9.735 31.590075
3.5 - 3.99 3.745 1 3.745 14.025025
4 - 4.49 4.245 2 8.49 36.04005
Total 46 75.77 179.61615

Mean, x̅ = ∑fx / n = 75.77/46 = 1.647

Standard deviation, s = √((∑fx² - (∑fx)²/n)/(n-1)) = √((179.6162 - 75.77²/46)/(46- 1)) = 1.1036

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