Question

the data to the right represent the number of people from a certain county, aged 5 to 64, who visited an optometrist over the course of last year.

(a) create a relative frequency distribution. (round to three decimal places as needed.)

(b) create a frequency histogram. choose the correct answer below.

Explanation:

🆕 New Concept Discovered: Relative Frequency Distribution
Proportion of data falling in each class

Step 1: Find the total number of patients

To find the relative frequency for each age group, we first need to calculate the total number of patients across all groups by summing the frequencies.

$$ \text{Total} = 2367 + 2952 + 6654 + 6479 = 18452 $$

Step 2: Calculate the relative frequency for each class

The relative frequency of a class is calculated by dividing the frequency of that class by the total number of observations:

$$ \text{Relative Frequency} = \frac{\text{Class Frequency}}{\text{Total Frequency}} $$

We will round each result to three decimal places.

• For Age 5–19:

$$ \frac{2367}{18452} \approx 0.12827 ightarrow 0.128 $$

• For Age 20–34:

$$ \frac{2952}{18452} \approx 0.15998 ightarrow 0.160 $$

• For Age 35–49:

$$ \frac{6654}{18452} \approx 0.36061 ightarrow 0.361 $$

• For Age 50–64:

$$ \frac{6479}{18452} \approx 0.35112 ightarrow 0.351 $$

Answer:

The completed relative frequency table is:

Age	Relative Frequency
20–34	0.160
35–49	0.361
50–64	0.351