Questions: Several years ago, the state of California launched an aggressive advertisement campaign against smoking. We've interviewed students from 18 college campuses in California and recorded for each campus the percentage of students who stated that they encountered at least one anti-smoking advertisement in the past month. Here are those percentages. 38,56,41,61,40,51,34,48,41,37,58,37,50,59,60,28,34,39 Send data to calculator Using the tool provided, construct a box-and-whisker plot (sometimes called a boxplot) for the data.

Several years ago, the state of California launched an aggressive advertisement campaign against smoking. We've interviewed students from 18 college campuses in California and recorded for each campus the percentage of students who stated that they encountered at least one anti-smoking advertisement in the past month. Here are those percentages.
38,56,41,61,40,51,34,48,41,37,58,37,50,59,60,28,34,39

Send data to calculator

Using the tool provided, construct a box-and-whisker plot (sometimes called a boxplot) for the data.
Transcript text: Several years ago, the state of California launched an aggressive advertisement campaign against smoking. We've interviewed students from 18 college campuses in California and recorded for each campus the percentage of students who stated that they encountered at least one anti-smoking advertisement in the past month. Here are those percentages. \[ 38,56,41,61,40,51,34,48,41,37,58,37,50,59,60,28,34,39 \] Send data to calculator Using the tool provided, construct a box-and-whisker plot (sometimes called a boxplot) for the data.
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Solution

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Solution Steps

Step 1: Organize the Data

First, we need to organize the given data in ascending order: \[34, 34, 37, 37, 38, 39, 40, 41, 41, 41, 48, 51, 56, 58, 59, 60, 61\]

Step 2: Calculate the Quartiles

To construct a box-and-whisker plot, we need to find the quartiles (Q1, Q2, Q3):

  • Q1 (First Quartile): The median of the first half of the data.
  • Q2 (Second Quartile/Median): The median of the entire data set.
  • Q3 (Third Quartile): The median of the second half of the data.

For the given data:

  • Q2 (Median): The middle value of the data set. Since there are 17 data points, the median is the 9th value: \(41\).
  • Q1: The median of the first 8 values: \(37\).
  • Q3: The median of the last 8 values: \(58\).
Step 3: Determine the Minimum and Maximum Values

Identify the minimum and maximum values in the data set:

  • Minimum: \(34\)
  • Maximum: \(61\)

Final Answer

Using the calculated quartiles and the minimum and maximum values, the box-and-whisker plot can be constructed with the following key points:

  • Minimum: \(34\)
  • Q1: \(37\)
  • Median (Q2): \(41\)
  • Q3: \(58\)
  • Maximum: \(61\)
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