Question

90 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. the (incomplete) results are shown below: # of times floss per week frequency relative frequency cumulative frequency 0 11 0.1222 11 1 9 0.1 20 2 14 0.1556 34 3 9 0.1 43 4 8 0.0889 51 5 12 0.1333 63 6 12 0.1333 75 7 15 1.6666 90 a. complete the table (use 4 decimal places when applicable) b. what is the cumulative relative frequency for flossing 7 times per week? %

Explanation:

Step1: Calculate relative - frequency correction for 7 times flossing

The sum of all frequencies is 90. The relative frequency of an event is calculated as $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total Frequency}}$. For 7 times flossing, the frequency is 15. So the relative frequency should be $\frac{15}{90}\approx0.1667$, not 1.6666.

Step2: Find cumulative relative frequency for 7 times flossing

The cumulative relative frequency is the sum of all relative frequencies up to that point. Since the total frequency is 90 and the sum of all relative frequencies of all categories should be 1 (or 100% when expressed as a percentage). The cumulative relative frequency for flossing 7 times per week is 1 or 100% because it includes all the data points.

Answer:

a. The corrected relative - frequency for 7 times flossing is 0.1667.
b. 100%