ms. redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest…

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.

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.

Answer

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 data values divided by number of data values.

Step2: Analyze the original data set

The original data set has (n = 10) data points. To find the median of 10 data points, we take the average of the 5th and 6th ordered data points.

Step3: Consider the new data set

When we add a new data point of (0.5) minutes, the number of data points becomes (n=11). The new median is the 6th ordered data point. Since the new value (0.5) is likely to be one of the smallest values, it may or may not change the position of the 6th ordered value (depending on the original values), but it will definitely pull the sum of the data values down. The formula for the mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}). When we add a new, relatively small value ((x_{new}=0.5)) and increase (n) by 1, the new mean (\bar{x}{new}=\frac{\sum{i = 1}^{10}x_{i}+0.5}{11}) will be smaller than the original mean (\bar{x}{old}=\frac{\sum{i = 1}^{10}x_{i}}{10}).

Answer:

The mean will decrease.