Question

construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in non - filtered and filtered cigarettes. do the cigarette filters appear to be effective? (hint: the filters reduce the amount of tar ingested by the smoker.)
click the icon to view the frequency distributions.
complete the following relative frequency table.
(round to the nearest percent as needed.)

tar (mg)	relative frequency (non - filtered)	relative frequency (filtered)
8 - 11	0%
12 - 15
16 - 19
20 - 23
24 - 27
28 - 31

frequency distributions

tar (mg) in non - filtered cigarettes	frequency	tar (mg) in filtered cigarettes	frequency
16 - 19	1	12 - 15	5
20 - 23	13	16 - 19	14
24 - 27	6
28 - 31	3

Explanation:

Step1: Calculate total frequencies for non - filtered and filtered

For non - filtered: $1 + 13+6 + 3=23$. For filtered: $3 + 5+14 = 22$.

Step2: Calculate relative frequencies for non - filtered

For $4 - 7$ mg: $\frac{1}{23}\times100\%\approx4\%$. For $8 - 11$ mg: $\frac{0}{23}\times100\% = 0\%$. For $12 - 15$ mg: $\frac{0}{23}\times100\% = 0\%$. For $16 - 19$ mg: $\frac{13}{23}\times100\%\approx57\%$. For $20 - 23$ mg: $\frac{6}{23}\times100\%\approx26\%$. For $24 - 27$ mg: $\frac{0}{23}\times100\% = 0\%$. For $28 - 31$ mg: $\frac{3}{23}\times100\%\approx13\%$.

Step3: Calculate relative frequencies for filtered

For $4 - 7$ mg: $\frac{0}{22}\times100\% = 0\%$. For $8 - 11$ mg: $\frac{3}{22}\times100\%\approx14\%$. For $12 - 15$ mg: $\frac{5}{22}\times100\%\approx23\%$. For $16 - 19$ mg: $\frac{14}{22}\times100\%\approx64\%$. For $20 - 23$ mg: $\frac{0}{22}\times100\% = 0\%$. For $24 - 27$ mg: $\frac{0}{22}\times100\% = 0\%$. For $28 - 31$ mg: $\frac{0}{22}\times100\% = 0\%$.

Answer:

Tar (mg)	Relative Frequency (Non - filtered)	Relative Frequency (Filtered)
$8 - 11$	$0\%$	$14\%$
$12 - 15$	$0\%$	$23\%$
$16 - 19$	$57\%$	$64\%$
$20 - 23$	$26\%$	$0\%$
$24 - 27$	$0\%$	$0\%$
$28 - 31$	$13\%$	$0\%$