Question

on core algebra i b-cr
englis
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.
monologue times
number of minutes
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: List original 10 data points

From the dot plot, the times are: 1, 1.5, 1.5, 2, 2, 2.5, 3, 3, 3.5, 3.5

Step2: Calculate original mean

$\text{Mean} = \frac{1+1.5+1.5+2+2+2.5+3+3+3.5+3.5}{10} = \frac{23}{10} = 2.3$

Step3: Calculate original median

For 10 values, median is average of 5th and 6th terms: $\frac{2+2.5}{2} = 2.25$

Step4: Add new data point (0.5), get 11 values

New data set: 0.5, 1, 1.5, 1.5, 2, 2, 2.5, 3, 3, 3.5, 3.5

Step5: Calculate new mean

$\text{New Mean} = \frac{23 + 0.5}{11} = \frac{23.5}{11} \approx 2.14$

Step6: Calculate new median

For 11 values, median is the 6th term: $2$

Step7: Compare changes

Mean decreases from 2.3 to ~2.14; median decreases from 2.25 to 2.

Answer:

The median will decrease.
The mean will decrease.