Question

the graph shows the number of pages in each chapter of a book that josh is reading.
chapter page counts
(the dot plot has a horizontal axis labeled number of pages from 2 to 29 with tick marks at 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 29. the dot plot has the following data: 2, 10, 10, 12, 14, 14, 14, 16, 16, 18, 20, 22, 28. wait, no, looking at the dots: at 2: 1 dot; at 10: 2 dots; at 12: 1 dot; at 14: 3 dots? wait the original: the first dot at 2, then two at 10, one at 12, three at 14? wait the users image: the dots are at 2 (1), 10 (2), 12 (1), 14 (3? wait no, the users image: the first dot at 2, then two dots at 10, one at 12, three at 14? wait the users ocr: the horizontal axis is 2,4,6,8,10,12,14,16,18,20,22,24,26,29. the dots: at 2: 1; at 10: 2; at 12: 1; at 14: 3? wait no, the users image: the first dot at 2, then two dots at 10, one at 12, three at 14? wait maybe better to re-express: the dot plot for chapter page counts, x-axis number of pages. dots: 2 (1), 10 (2), 12 (1), 14 (3), 16 (2), 20 (1), 22 (1), 28 (1)? wait no, the users image: the first dot at 2, then two at 10, one at 12, three at 14? wait the users question: which statement is true about the effect of the 2 - page introduction chapter?
options:

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

Explanation:

Step1: Recall Median and Mean Properties

Median is the middle value (or average of two middle values) in an ordered data set. It's resistant to outliers (extreme values) because it depends on the position of values, not their magnitude. Mean is the sum of all values divided by the number of values, so it's sensitive to outliers.

Step2: Analyze Outlier (2 pages) Impact on Median

The outlier (2) is a small value. When ordering data, the median's position (middle) doesn't shift much because median depends on count of values, not their size. So the outlier doesn't increase or decrease the median significantly.

Step3: Analyze Outlier (2 pages) Impact on Mean

Mean = $\frac{\text{Sum of all values}}{\text{Number of values}}$. The outlier (2) is much smaller than most other values. Adding a small value (lower than the typical data) will decrease the total sum, thus decreasing the mean (since the number of values increases by 1, but the sum decreases more relatively).

Answer:

The outlier of 2 decreases the mean page count.