the graph shows the number of minutes, to the nearest five minutes, that sarah spent getting ready for…

Explanation:

Step1: List the original data points from the dot plot.

The data points are: 25, 30, 35, 35, 45, 45, 45, 50, 50, 55, 55, 55. There are $n=12$ data points.

Step2: Calculate the original mean.

$$ \text{Mean}{\text{original}} = \frac{25 + 30 + 2(35) + 3(45) + 2(50) + 3(55)}{12} $$ $$ \text{Mean}{\text{original}} = \frac{25 + 30 + 70 + 135 + 100 + 165}{12} = \frac{525}{12} = 43.75 $$

Step3: Calculate the original median.

Order the data: 25, 30, 35, 35, 45, 45, 45, 50, 50, 55, 55, 55. Since $n=12$ (even), the median is the average of the 6th and 7th values. $$ \text{Median}_{\text{original}} = \frac{45 + 45}{2} = 45 $$

Step4: Add the new data point (15) to the dataset.

The new data set is: 15, 25, 30, 35, 35, 45, 45, 45, 50, 50, 55, 55, 55. There are now $n=13$ data points.

Step5: Calculate the new mean.

$$ \text{Mean}_{\text{new}} = \frac{525 + 15}{13} = \frac{540}{13} \approx 41.54 $$

Step6: Calculate the new median.

Order the new data: 15, 25, 30, 35, 35, 45, 45, 45, 50, 50, 55, 55, 55. Since $n=13$ (odd), the median is the middle value, which is the 7th value. $$ \text{Median}_{\text{new}} = 45 $$

Step7: Compare the original and new mean and median.

The mean decreased from 43.75 to approximately 41.54. The median remained the same at 45.

Answer:

The mean will decrease, and the median will stay the same.