construct one table that includes relative frequencies based on the frequency distributions shown below…
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.)\nclick the icon to view the frequency distributions.\ncomplete the following relative frequency table.\n(round to the nearest percent as needed.)\n| tar (mg) | relative frequency (non - filtered) | relative frequency (filtered) |\n| ---- | ---- | ---- |\n| 4 - 7 | | |\n| 8 - 11 | 0% | |\n| 12 - 15 | | |\n| 16 - 19 | | |\n| 20 - 23 | | |\n| 24 - 27 | | |\n| 28 - 31 | | |\nfrequency distributions\n| tar (mg) in non - filtered cigarettes | frequency | tar (mg) in filtered cigarettes | frequency |\n| ---- | ---- | ---- | ---- |\n| 12 - 15 | 1 | 8 - 11 | 3 |\n| 16 - 19 | 1 | 12 - 15 | 5 |\n| 20 - 23 | 13 | 16 - 19 | 14 |\n| 24 - 27 | 6 | | |\n| 28 - 31 | 3 | | |
Answer
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) |
|---|---|---|
| $4 - 7$ | $4%$ | $0%$ |
| $8 - 11$ | $0%$ | $14%$ |
| $12 - 15$ | $0%$ | $23%$ |
| $16 - 19$ | $57%$ | $64%$ |
| $20 - 23$ | $26%$ | $0%$ |
| $24 - 27$ | $0%$ | $0%$ |
| $28 - 31$ | $13%$ | $0%$ |