To address this question, we need to analyze the data provided for the number of vacation days Matt and Linda have remaining at the end of each quarter. We will calculate the median and mean of their remaining vacation days.
#### Step 1: Data Extraction
- Matt's remaining vacation days per quarter: 13, 11, 7, 4
- Linda's remaining vacation days per quarter: 12, 11, 7, 0
#### Step 2: Calculate the Median
Median for Matt:
- Order Matt's days: 4, 7, 11, 13
- The median (middle value) when the number of observations is even is the average of the two middle numbers. For Matt:
[tex]\[
\text{Median for Matt} = \frac{7 + 11}{2} = 9.0
\][/tex]
Median for Linda:
- Order Linda's days: 0, 7, 11, 12
- The median for Linda is:
[tex]\[
\text{Median for Linda} = \frac{7 + 11}{2} = 9.0
\][/tex]
#### Step 3: Calculate the Mean
Mean for Matt:
- Mean is the sum of all values divided by the number of values. For Matt:
[tex]\[
\text{Mean for Matt} = \frac{13 + 11 + 7 + 4}{4} = \frac{35}{4} = 8.75
\][/tex]
Mean for Linda:
- For Linda:
[tex]\[
\text{Mean for Linda} = \frac{12 + 11 + 7 + 0}{4} = \frac{30}{4} = 7.5
\][/tex]
#### Step 4: Compare and Determine the Correct Statement
- Median Matt = 9.0
- Median Linda = 9.0
Since both medians are equal, neither A nor B is true.
- Mean Matt = 8.75
- Mean Linda = 7.5
Since Matt's mean is greater than Linda's mean, statement C is true.
- Since the medians are equal (not greater) and the mean for Matt is greater than the mean for Linda, statement D is false.
Therefore, the correct statement is:
C. The mean number of vacation days Matt has remaining is greater than the mean number of vacation days Linda has remaining.
