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? the median will decrease. the mean will decrease. the median will increase. the mean will increase.

Explanation:

Step1: Recall median and mean concepts

Median is middle - value (for odd number of data points) or average of two middle - values (for even number of data points). Mean is sum of all data points divided by number of data points.

Step2: Analyze original data

We have 10 data points. For 10 data points, median is average of 5th and 6th ordered data points. Mean is $\frac{\sum_{i = 1}^{10}x_i}{10}$, where $x_i$ are the monologue times.

Step3: Add new data point

We add a new data point of 0.5 minutes. Now we have 11 data points. The new median is the 6th ordered data point. Since 0.5 is likely to be one of the smallest values, it won't change the position of the middle value (6th value) in a way that median decreases or increases significantly. But for the mean, $\sum_{i = 1}^{11}x_i=\sum_{i = 1}^{10}x_i + 0.5$. Since 0.5 is smaller than most of the original values, the new mean $\frac{\sum_{i = 1}^{10}x_i+0.5}{11}<\frac{\sum_{i = 1}^{10}x_i}{10}$ (because adding a small value and increasing the denominator by 1 makes the fraction smaller).

Answer:

The mean will decrease