Question

Construct one table that includes relative frequencies based on the frequency distributions shown​ below, then compare the amounts of tar in nonfiltered and filtered cigarettes. Do the cigarette filters appear to be​ effective? (Hint: The filters reduce the amount of tar ingested by the​ smoker.)

Tar​ (mg) in Nonfiltered Cigarettes	Frequency		Tar​ (mg) in Filtered Cigarettes	Frequency
14minus−18	2		4minus−8	1
19minus−23	0		9minus−13	2
24minus−28	15		14minus−18	5
29minus−33	7		19minus-23	17
34minus−38	1

Complete the relative frequency table below.

Tar Relative Frequency(unfiltered) Relative Frequency (filtered)

4-8. % %

9-13 % %

14-18 % %

19-23 % %

24-28 % %

29-33 % %

34-38 % %

Answer 1

The relative Frequencies are computed by dividing each of the frequencies with the total frequency of that group. Therefore the relative frequency shows the share of total frequencies in that particular class.

Total Frequency ( Non - filtered ) = 2 + 0 + 15 + 7 + 1 = 25
Total Frequency (Filtered) = 1 + 2 + 5 + 17 = 25

Interval	Relative Frequency (unfiltered)	Relative Frequency (filtered)
4-8	0	1/25 = 4%
9-13	0	2/25 = 8%
14-18	2/25 = 8%	5/25 = 20%
19-23	0	17/25 = 68%
24-28	15/25 = 60%	0
29-33	7/25 = 28%	0
34-38	1/25 = 4%	0

This is the required set of relative frequencies here.

Clearly as the higher percentage values lies on the upper side of the table for the filtered ones compared to the non filtered ones, therefore yes the filter appears to be effective here.