Question

the graph shows the number of pages in each chapter of a book that josh is reading.

which statement is true about the effect of the 2-page introduction chapter?

• the outlier of 2 decreases the mean page count.
• the outlier of 2 increases the median page count.
• the outlier of 2 decreases the median page count.
• the outlier of 2 increases the mean page count.

Explanation:

Identify the data set and the outlier

The dot plot shows the page counts of chapters:

• One dot at \(2\) (the outlier)
• Two dots at \(10\)
• Three dots at \(14\)
• Two dots at \(16\)
• One dot at \(18\)
• Two dots at \(20\)
• Two dots at \(22\)
• One dot at \(26\)

The value \(2\) is significantly smaller than the rest of the data points, making it a low outlier.

Analyze the effect of a low outlier on measures of center

• A low outlier pulls the mean (average) down, meaning it decreases the mean page count.
• The median is resistant to outliers, so its value remains relatively unaffected compared to the mean.
• Therefore, the outlier of \(2\) decreases the mean page count.

Answer:

• The outlier of 2 decreases the mean page count. (Correct answer)
• The outlier of 2 increases the median page count.
• The outlier of 2 decreases the median page count.
• The outlier of 2 increases the mean page count.