Question

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 y = $1.545 and standard deviation o = $0.941 Click the icon to view the frequency distribution for the tax rates The population mean is $ (Round to three decimal places as needed.) The population standard deviation is s (Round to three decimal places as needed) Compare these results to the values found using the actual data O A. The grouped mean is slightly larger, while the grouped standard deviation is slightly smaller. B. The grouped values are both slightly smaller O C. The grouped values are both slightly larger OD. The grouped mean is slightly smaller while the grouped standard deviation is slightly larger Click to select your answer(s).

Answer 1

Solution-

The population mean is $ 1.588

◆ Calculation-

Class Frequency (f) Mid value (x) (1) (2) (3) f:x (4) = (2) × (3) f.x2 = (f.x) * (x) cf (5) = (4) (3) (6) 0-0.49 6 0.245 1.47 0.3601 6 0.5-0.99 14 0.745 10.43 7.7704 20 1-1.49 8 1.245 9.96 12.4002 28 1.5-1.99 8 1.745 13.96 24.3602 36 2-2.49 8 2.245 17.96 40.3202 44 2.5-2.99 4 2.745 10.98 30.1401 48 3-3.49 4 3.245 12.98 42.1201 52 3.5-3.99 3.745 3.745 14.025 53 1 1 4-4.49 4.245 4.245 18.02 54 --- -- n = 54 Ef. x = 85.73 Ef. x2 = 189.5164 --

Σfx Mean X = n 85.73 54 1.5876

The population standard deviation is $ 0.995

◆ Calculation-

(f-x)2 £f.x2. Population Standard deviation o = n 2 (85.73) 189.5164 - 54 54 189.5164 - 136.1043 54 153.412 54 = 0.9891 = 0.9945

Comparison-

● C. The grouped values of both are slightly larger.