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. monologue times 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 number of minutes

Explanation:

Step1: Recall median and mean concepts

Median is middle - value, mean is sum/number of data points.

Step2: Analyze data set size and values

Original data set has $n = 10$ data points. After adding a 0.5 - minute monologue, $n=11$. Original data seems to be centered around 2 - 3 minutes.

Step3: Consider effect on median

For $n = 10$ (even), median is average of 5th and 6th ordered values. For $n = 11$ (odd), median is 6th ordered value. Since 0.5 is a low - value, it won't change the position of the middle value much in terms of order, so median may not change significantly.

Step4: Consider effect on mean

Let sum of original 10 data points be $S$. Original mean $\bar{x}_1=\frac{S}{10}$. New sum is $S + 0.5$ and new mean $\bar{x}_2=\frac{S + 0.5}{11}$. Since 0.5 is a relatively small value compared to the sum of the original data (which seems to have values mostly around 2 - 3 minutes), and we are dividing by a larger number (11 instead of 10), the new mean will be smaller.

Answer:

The mean will decrease.