An instructor recommends to students in his introductory statistics class to spend at least 5 hours studying outside class. One of the items on the student survey for this course was "How many hours a week do you study for this class?” The instructor examined the data for men and women separately. Below is the distribution of this variable for the 30 women in the class.Part C: Which of the following boxplots represents the same data set as the histogram shown above?
Question
An instructor recommends to students in his introductory statistics class to spend at least 5 hours studying outside class. One of the items on the student survey for this course was "How many hours a week do you study for this class?” The instructor examined the data for men and women separately. Below is the distribution of this variable for the 30 women in the class.Part C: Which of the following boxplots represents the same data set as the histogram shown above?
Solution
To determine which boxplot represents the same data set as the histogram shown, follow these steps:
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Examine the Histogram: Look at the histogram to understand the distribution of the data. Note the range, the median, and the spread of the data.
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Identify Key Features:
- Range: Identify the minimum and maximum values.
- Median: Determine the median value, which is the middle value when the data is ordered.
- Quartiles: Identify the first quartile (Q1) and the third quartile (Q3). These are the medians of the lower and upper halves of the data, respectively.
- Outliers: Note any outliers, which are data points that fall significantly outside the range of the rest of the data.
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Compare with Boxplots:
- Range: Check if the range of the boxplot matches the range of the histogram.
- Median: Ensure the median line in the boxplot corresponds to the median observed in the histogram.
- Quartiles: Verify that the interquartile range (IQR), which is the distance between Q1 and Q3, matches the spread of the central 50% of the data in the histogram.
- Outliers: Confirm that any outliers in the histogram are also represented in the boxplot.
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Select the Matching Boxplot: Choose the boxplot that accurately reflects the range, median, quartiles, and outliers observed in the histogram.
By carefully comparing these features, you can identify which boxplot corresponds to the data set represented by the histogram.
Similar Questions
An instructor recommends to students in his introductory statistics class to spend at least 5 hours studying outside class. One of the items on the student survey for this course was "How many hours a week do you study for this class?” The instructor examined the data for men and women separately. Below is the distribution of this variable for the 30 women in the class.Part A: How should the instructor interpret the amount of time that women spend studying for the class? There can be more than one correct answer. Please answer all that apply. Group of answer choicesA majority of women in the class spend less than the recommended number of hours studying although a few women do take the instructors advice.The women in the class study less than the men in the class.If you remove the three women with the highest number of study hours, then the result will show an approximately normal distribution.
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