Question

question 21
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 0.0889 8
1 15 0.1667 23
2 13 0.1444 36
3 10 0.1111
4 14 0.1556 60
5 10 0.1111 70
6 10 80
7 10 0.1111 90
a. complete the table (use 4 decimal places when applicable)
b. what is the cumulative relative frequency for flossing 6 times per week?

Explanation:

Step1: Find the frequency for 0 times floss per week

We know that relative - frequency = $\frac{\text{frequency}}{\text{total number of data points}}$. The total number of data points is $n = 90$. Given the relative frequency for 0 times floss per week is $0.0889$. So the frequency for 0 times floss per week is $0.0889\times90=8$.

Step2: Find the cumulative frequency for 3 times floss per week

The cumulative frequency is the sum of the frequencies of all values less than or equal to the current value. For 3 times floss per week, we know that the cumulative frequency up to 2 times floss per week is 36 and the frequency for 3 times floss per week is 10. So the cumulative frequency for 3 times floss per week is $36 + 10=46$.

Step3: Find the relative frequency for 6 times floss per week

Relative - frequency = $\frac{\text{frequency}}{\text{total number of data points}}$. The frequency for 6 times floss per week is 10 and the total number of data points is 90. So the relative frequency for 6 times floss per week is $\frac{10}{90}\approx0.1111$.

Step4: Find the cumulative relative frequency for 6 times floss per week

The cumulative relative frequency is the sum of the relative frequencies of all values less than or equal to the current value.
The cumulative relative frequency for 5 times floss per week is $\frac{70}{90}\approx0.7778$. The relative frequency for 6 times floss per week is $\frac{10}{90}\approx0.1111$. So the cumulative relative frequency for 6 times floss per week is $0.7778+0.1111 = 0.8889$.

Answer:

a.

# of times floss per week	Frequency	Relative Frequency	Cumulative Frequency
1	15	0.1667	23
2	13	0.1444	36
3	10	0.1111	46
4	14	0.1556	60
5	10	0.1111	70
6	10	0.1111	80
7	10	0.1111	90

b. 0.8889