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 u=​$1.601 and standard deviation O= ​$1.078.

Tax Rate	Lower Limit	Upper Limit	Frequency
0.00-0.49	0	0.49	7
0.50-0.99	0.5	0.99	15
1.00-1.49	1	1.49	6
1.50-1.99	1.5	1.99	7
2.00-2.49	2	2.49	6
2.50-2.99	2.5	2.99	5
3.00-3.49	3	3.49	4
3.50-3.99	3.5	3.99	2
4.00-4.49	4	4.49	2

1a. The population mean is $_____

1b. The population standard deviation is $. (Round to three decimal places as​ needed.)

1c. Compare these results to the values found using the actual data.

A.

The grouped values are both slightly smaller.

B.

The grouped mean is slightly​ larger, while the grouped standard deviation is slightly smaller.

C.

The grouped values are both slightly larger.

D.

The grouped mean is slightly​ smaller, while the grouped standard deviation is slightly larger.

Answer 1

Tax Rate	Lower Limit	Upper Limit	Mid value (x)	Frequency (f)	x*f	x^2*f
0.00-0.49	0	0.49	0.245	7	1.715	0.420175
0.50-0.99	0.5	0.99	0.745	15	11.175	8.325375
1.00-1.49	1	1.49	1.245	6	7.47	9.30015
1.50-1.99	1.5	1.99	1.745	7	12.215	21.31518
2.00-2.49	2	2.49	2.245	6	13.47	30.24015
2.50-2.99	2.5	2.99	2.745	5	13.725	37.67513
3.00-3.49	3	3.49	3.245	4	12.98	42.1201
3.50-3.99	3.5	3.99	3.745	2	7.49	28.05005
4.00-4.49	4	4.49	4.245	2	8.49	36.04005
			Total	54	88.73	213.4864

1a. The population mean is $ 1.64

1b. The population standard deviation is $ 1.120.

1c. Option: C. The grouped values are both slightly larger.