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The box plot shows the result of a survey of the ages of several trees in a local park.

A number line going from 10 to 85 in increments of 5 labeled every 15 years. A box plot with a whisker going from the minimum of 15 years to the lower quartile of 30 years. A box going from the lower quartile of 30 years to the upper quartile of 70 years with a median at 45 years. A whisker going from 70 years to a maximum of 85 years.

Which statement is true?

(1 point)
Responses

The range of the tree ages is 45 years. The median tree age is 45 years. The lower quartile is 30 years, and the upper quartile is 70 years.
The range of the tree ages is 45 years. The median tree age is 45 years. The lower quartile is 30 years, and the upper quartile is 70 years.

The range of the tree ages is 70 years. The median tree age is 45 years. The lower quartile is 15 years, and the upper quartile is 85 years.
The range of the tree ages is 70 years. The median tree age is 45 years. The lower quartile is 15 years, and the upper quartile is 85 years.

The range of the tree ages is 70 years. The median tree age is 45 years. The lower quartile is 30 years, and the upper quartile is 70 years.
The range of the tree ages is 70 years. The median tree age is 45 years. The lower quartile is 30 years, and the upper quartile is 70 years.

The range of the tree ages is 70 years. The median tree age is 55 years. The lower quartile is 30 years, and the upper quartile is 70 years.
The range of the tree ages is 70 years. The median tree age is 55 years. The lower quartile is 30 years, and the upper quartile is 70 years.
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1 answer

To determine the correct response from the given statements, let's break down the information provided in the description of the box plot:

  1. Range of Tree Ages: The range is calculated as the maximum age minus the minimum age. Here, the minimum age is 15 years, and the maximum age is 85 years. Thus, the range is: \[ \text{Range} = 85 - 15 = 70 \text{ years} \]

  2. Median Tree Age: The median age represented in the box plot is given as 45 years.

  3. Lower Quartile and Upper Quartile: According to the description:

    • The lower quartile (Q1) is 30 years.
    • The upper quartile (Q3) is 70 years.

Given that we've found:

  • Range = 70 years
  • Median = 45 years
  • Lower quartile = 30 years
  • Upper quartile = 70 years

Now, we can analyze the options to find which statement is true:

  1. Statement A: Range = 45 years, Median = 45 years, lower quartile = 30 years, upper quartile = 70 years.

    • Incorrect (the range is not 45 years).

  2. Statement B: Range = 70 years, Median = 45 years, lower quartile = 15 years, upper quartile = 85 years.

    • Incorrect (the lower quartile and upper quartile are wrong).

  3. Statement C: Range = 70 years, Median = 45 years, lower quartile = 30 years, upper quartile = 70 years.

    • Correct (all values match).

  4. Statement D: Range = 70 years, Median = 55 years, lower quartile = 30 years, upper quartile = 70 years.

    • Incorrect (the median is not 55 years).

Therefore, the correct answer is:

The range of the tree ages is 70 years. The median tree age is 45 years. The lower quartile is 30 years, and the upper quartile is 70 years.