Math  /  Data & Statistics

QuestionA researcher recorded the amount of time, rounded to the nearest second, that it took each of 14 people to complete a certain task. The recorded times are summarized in the boxplot shown. Which of the following statements must be true?
Indicate all such statements. At least one person had a recorded time of 25 seconds. At least one person had a recorded time of 50 seconds. Each of the 14 people had a recorded time of at most 60 seconds. select one or more answer choices.

Studdy Solution

STEP 1

Assumptions
1. The boxplot represents the recorded times of 14 people completing a task.
2. The minimum recorded time is 25 seconds.
3. The first quartile (Q1) is at 30 seconds.
4. The median (Q2) is at 40 seconds.
5. The third quartile (Q3) is at 50 seconds.
6. The maximum recorded time is 60 seconds.
7. The times are rounded to the nearest second.

STEP 2

We need to verify the statement: "At least one person had a recorded time of 25 seconds."
Since the minimum time shown on the boxplot is 25 seconds, this means that at least one person had a recorded time of 25 seconds.
Thus, this statement is true.

STEP 3

We need to verify the statement: "At least one person had a recorded time of 50 seconds."
Since the third quartile (Q3) is at 50 seconds, this means that at least 25% of the recorded times are less than or equal to 50 seconds, and at least 75% of the recorded times are greater than or equal to 50 seconds. Therefore, at least one person had a recorded time of 50 seconds.
Thus, this statement is true.

STEP 4

We need to verify the statement: "Each of the 14 people had a recorded time of at most 60 seconds."
Since the maximum time shown on the boxplot is 60 seconds, this means that no recorded time exceeds 60 seconds.
Thus, this statement is true.

STEP 5

Summarize the results. All three statements must be true based on the given boxplot.
1. At least one person had a recorded time of 25 seconds.
2. At least one person had a recorded time of 50 seconds.
3. Each of the 14 people had a recorded time of at most 60 seconds.

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