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.

\

$$\begin{tabular}{|c|c|} \\hline age & patients \\\\ \\hline 5-19 & 2367 \\\\ 20-34 & 2952 \\\\ 35-49 & 6654 \\\\ 50-64 & 6479 \\\\ \\hline \\end{tabular}$$

choose the correct histogram representing the data.

a.
b.
c.
d.

Explanation:

⚡ Using what you learned: Organizing Data in Tables · 🆕 New: Histograms
Visualizing grouped frequency data using adjacent bars

Step 1: Analyze the Frequency Table

We are given a frequency table showing the number of patients in different age groups:

Age Group	Patients (Frequency)
20–34	2952
35–49	6654
50–64	6479

Step 2: Match the Data to the Graph Options

Let's look at the height of the bars for each age group in the options:

1. First class (5–19): The frequency is \( 2367 \). The bar should be slightly above \( 2000 \).
2. Second class (20–34): The frequency is \( 2952 \). The bar should be just below \( 3000 \).

• Comparing the first two classes: The second bar (\( 2952 \)) must be taller than the first bar (\( 2367 \)).

1. Third class (35–49): The frequency is \( 6654 \). This is the tallest bar, reaching well above \( 6000 \).
2. Fourth class (50–64): The frequency is \( 6479 \). This bar is slightly shorter than the third bar but still well above \( 6000 \).

Step 3: Evaluate the Choices

• Graph A:
• First bar (5–19) is around \( 2300 \).
• Second bar (20–34) is around \( 2900 \) (taller than the first).
• Third bar (35–49) is the tallest, over \( 6000 \).
• Fourth bar (50–64) is slightly shorter than the third, also over \( 6000 \).
• This matches our data perfectly.

• Graph B:
• The first bar is much taller than the second bar, which is incorrect because \( 2367 < 2952 \).

• Graph C:
• The third and fourth bars are below \( 5000 \), which is incorrect because both values (\( 6654 \) and \( 6479 \)) are well above \( 6000 \).

• Graph D:
• The first bar is taller than the second bar, and the fourth bar is much too short (around \( 3000 \)).

Therefore, Graph A is the correct representation.

Answer:

A