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.

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

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

Explanation:

⚡ Using what you learned: displaying data: histograms & box plots

Step 1: Calculate the total number of patients

Sum the frequencies for all age groups:

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

Step 2: Calculate the relative frequencies

Divide the frequency of each class by the total count:

• Age 5–19:

$$ \frac{2367}{18452} \approx 0.128 \quad (12.8\%) $$

• Age 20–34:

$$ \frac{2952}{18452} \approx 0.160 \quad (16.0\%) $$

• Age 35–49:

$$ \frac{6654}{18452} \approx 0.361 \quad (36.1\%) $$

• Age 50–64:

$$ \frac{6479}{18452} \approx 0.351 \quad (35.1\%) $$

Step 3: Match with the correct histogram

• The first bar (5–19) should be at approximately \(0.13\).
• The second bar (20–34) should be slightly higher, at approximately \(0.16\).
• The third bar (35–49) should be the tallest, at approximately \(0.36\).
• The fourth bar (50–64) should be slightly lower than the third, at approximately \(0.35\).

Comparing the options:

• Graph A: The first bar is around \(0.10\), the second is slightly higher, the third is around \(0.25\), and the fourth is around \(0.23\). This does not match the peak values of \(0.36\) and \(0.35\).
• Graph B: The first bar is the tallest, which is incorrect.
• Graph C: The first bar is around \(0.13\), the second is around \(0.16\), the third is around \(0.36\), and the fourth is around \(0.35\). This matches our calculated relative frequencies perfectly.
• Graph D: The first bar is the tallest, which is incorrect.

Answer:

C