Questions: 110 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 13 0.1182 13 1 16 0.1455 29 2 18 0.1636 47 3 12 0.1091 59 4 15 74 5 13 0.1182 6 0.1091 99 7 11 0.1 110 a. Complete the table (Use 4 decimal places when applicable) b. What is the cumulative relative frequency for flossing 4 times per week? %

110 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 13 0.1182 13
1 16 0.1455 29
2 18 0.1636 47
3 12 0.1091 59
4 15 74
5 13 0.1182
6 0.1091 99
7 11 0.1 110

a. Complete the table (Use 4 decimal places when applicable)
b. What is the cumulative relative frequency for flossing 4 times per week? %

Transcript text: 110 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: \begin{tabular}{|c|c|c|c|} \hline \begin{tabular}{c} \# of times \\ floss per \\ week \end{tabular} & Frequency & \begin{tabular}{c} Relative \\ Frequency \end{tabular} & \begin{tabular}{c} Cumulative \\ Frequency \end{tabular} \\ \hline 0 & 13 & 0.1182 & 13 \\ \hline 1 & 16 & 0.1455 & 29 \\ \hline 2 & 18 & 0.1636 & 47 \\ \hline 3 & 12 & 0.1091 & 59 \\ \hline 4 & 15 & & 74 \\ \hline 5 & 13 & 0.1182 & \\ \hline 6 & & 0.1091 & 99 \\ \hline 7 & 11 & 0.1 & 110 \\ \hline \end{tabular} a. Complete the table (Use 4 decimal places when applicable) b. What is the cumulative relative frequency for flossing 4 times per week? $\square$ \%

Solution

Solution Steps

Step 1: Complete the Relative Frequency for Flossing 4 Times per Week

The relative frequency is calculated as: \[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Number of Adults}} \] For flossing 4 times per week: \[ \text{Relative Frequency} = \frac{15}{110} = 0.1364 \]

Step 2: Complete the Cumulative Frequency for Flossing 5 Times per Week

The cumulative frequency is the sum of all frequencies up to and including the current row. For flossing 5 times per week: \[ \text{Cumulative Frequency} = 74 + 13 = 87 \]

Step 3: Complete the Frequency for Flossing 6 Times per Week

The frequency can be calculated using the relative frequency: \[ \text{Frequency} = \text{Relative Frequency} \times \text{Total Number of Adults} \] For flossing 6 times per week: \[ \text{Frequency} = 0.1091 \times 110 = 12 \]

Step 4: Calculate the Cumulative Relative Frequency for Flossing 4 Times per Week

The cumulative relative frequency is the sum of all relative frequencies up to and including the current row. For flossing 4 times per week: \[ \text{Cumulative Relative Frequency} = 0.1182 + 0.1455 + 0.1636 + 0.1091 + 0.1364 = 0.6728 \] Convert this to a percentage: \[ \text{Cumulative Relative Frequency} = 0.6728 \times 100 = 67.28\% \]

Step 5: Finalize the Table

The completed table is as follows:

\[ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \# \text{ of times} \\ \text{floss per} \\ \text{week} \end{array} & \text{Frequency} & \begin{array}{c} \text{Relative} \\ \text{Frequency} \end{array} & \begin{array}{c} \text{Cumulative} \\ \text{Frequency} \end{array} \\ \hline 0 & 13 & 0.1182 & 13 \\ \hline 1 & 16 & 0.1455 & 29 \\ \hline 2 & 18 & 0.1636 & 47 \\ \hline 3 & 12 & 0.1091 & 59 \\ \hline 4 & 15 & 0.1364 & 74 \\ \hline 5 & 13 & 0.1182 & 87 \\ \hline 6 & 12 & 0.1091 & 99 \\ \hline 7 & 11 & 0.1 & 110 \\ \hline \end{array} \]