Question

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table $1.34.$

a. Fill in the blanks in Table$1.34.$

b. What percent of adults flossed six times per week?

c. What percent flossed at most three times per week?

Short answer

(a)

# Flossing per week	Frequency	Relative Frequency	Cumulative Frequency
0	27	0.4500	0.4500
1	18	0.3000	0.7500
3	11	0.1833	0.9333
6	3	0.0500	0.9833
7	1	0.0167	1.000

(b) Percent of adults who flossed $6$times a week is $5\%$

(c) Percent of adults who flossed at most $3$times a week is $93.33\%$

Step-by-step solution

Given information (part a)

Given a table with frequency and the number of times per week they used to floss.

Explanation (part a)

$$\begin{gathered} \text{Frequencyfor3}=60-27-18-3-1 \\ =11 \end{gathered}$$

$\text{Relativefrequency}=\frac{frequencyofthatclass}{totatfrequency}$

$$\begin{gathered} \text{Relativefrequencyof}1=\frac{18}{60} \\ =0.3000 \\ \text{Relativefrequencyof}3=\frac{11}{60} \\ =0.1833 \\ \text{Relativefrequencyof}6=\frac{3}{60} \\ =0.0500 \\ \text{Relativefrequencyof}7=\frac{1}{60} \\ =0.0167 \end{gathered}$$

$$\begin{gathered} \text{Cumulativefrequencyof}0=0.4500 \\ \text{Cumulativefrequencyof}3=0.75+0.183 \\ =0.9333 \\ \text{Cumulativefrequencyof}6=0.05+0.933 \\ =0.9833 \\ \text{Cumulativefrequencyof}7=0.983+0.0167 \\ =1.000 \end{gathered}$$

# Flossing per week	Frequency	Relative Frequency	Cumulative Frequency
0	27	0.4500	0.4500
1	18	0.3000	0.7500
3	11	0.1833	0.9333
6	3	0.0500	0.9833
7	1	0.0167	1.000

Given information (part b)

The number of adults who flosses $6$times is $3$and the total number of adults is $60$

Explanation (part b)

$$\begin{gathered} \text{Percent}=\frac{\text{number of adults who flossed}6\text{times}}{\text{total number of adults}}\times 100 \\ =\frac{3}{60}\times 100 \\ =5\% \end{gathered}$$

Given information (part c)

the number of adults who flossed $0,1\text{or}3$times is $27,18\text{and}11$respectively and total number of adults is $60$.

Explanation (part c)

$$\begin{gathered} \text{Percent}=\frac{\text{number of adults who flossedatmost3times}}{\text{total number of adults}}\times 100 \\ =\frac{27+18+11}{60}\times 100 \\ =93.33\% \end{gathered}$$