Question

ms. redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. the graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented. the next student presents a monologue that is about 0.5 minutes long. what effect will this have on the graph? monologue times the median will decrease. the mean will decrease. the median will increase. the mean will increase.

Explanation:

Step1: Analyze the median

There are 10 data - points initially. The median of 10 data - points is the average of the 5th and 6th ordered data - points. Adding a new data - point (0.5 minutes) which is likely to be one of the smallest values will not change the position of the 5th and 6th ordered data - points (when all 11 data - points are ordered), so the median will not change.

Step2: Analyze the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Initially, $n = 10$ and $\sum_{i=1}^{10}x_{i}$ is the sum of the first 10 monologue times. After adding a new data - point $x_{11}=0.5$, the new mean $\bar{x}_{new}=\frac{\sum_{i = 1}^{10}x_{i}+0.5}{11}$. Since 0.5 is likely to be smaller than the original mean, the new mean will decrease.

Answer:

The mean will decrease.