Question

the following data represent the number of potholes on 35 randomly selected 1-mile stretches of highway around a particular city. complete parts (a) through (d).

number of potholes
1 4 3 1 4
7 5 1 3 6
1 2 2 1 2
7 1 6 2 7
1 6 4 4 1
1 5 3 6 2
3 2 7 1 3

(a) construct a frequency distribution of the data.

potholes	frequency
2	6
3	5
4	4
5	2
6	4
7	4

(b) construct a relative frequency distribution of the data.

potholes	relative frequency
2
3
4
5
6
7

(round to three decimal places as needed.)

Explanation:

Part (b)

Step 1: Recall the formula for relative frequency

The relative frequency of a class is calculated as the frequency of the class divided by the total number of observations. The total number of observations here is 35 (since there are 35 1 - mile stretches). The formula for relative frequency ($rf$) is $rf=\frac{\text{Frequency}(f)}{\text{Total number of observations}(N)}$, where $N = 35$.

Step 2: Calculate relative frequency for Potholes = 1

The frequency for Potholes = 1 is 10. So, the relative frequency is $\frac{10}{35}\approx0.286$.

Step 3: Calculate relative frequency for Potholes = 2

The frequency for Potholes = 2 is 6. So, the relative frequency is $\frac{6}{35}\approx0.171$.

Step 4: Calculate relative frequency for Potholes = 3

The frequency for Potholes = 3 is 5. So, the relative frequency is $\frac{5}{35}\approx0.143$.

Step 5: Calculate relative frequency for Potholes = 4

The frequency for Potholes = 4 is 4. So, the relative frequency is $\frac{4}{35}\approx0.114$.

Step 6: Calculate relative frequency for Potholes = 5

The frequency for Potholes = 5 is 2. So, the relative frequency is $\frac{2}{35}\approx0.057$.

Step 7: Calculate relative frequency for Potholes = 6

The frequency for Potholes = 6 is 4. So, the relative frequency is $\frac{4}{35}\approx0.114$.

Step 8: Calculate relative frequency for Potholes = 7

The frequency for Potholes = 7 is 4. So, the relative frequency is $\frac{4}{35}\approx0.114$.

Answer:

Potholes	Relative Frequency
2	0.171
3	0.143
4	0.114
5	0.057
6	0.114
7	0.114