Question

Ms Redmond 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

Answer 1

The mean will decrease.

Answer 2

The correct option is B.

Explanation:

From the given dot plot we can create a frequency table.

x f

1.5 2

2 1

2.5 3

3 1

3.5 2

4 1

This data can be written as

1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4

The mean of the data is

`Mean=(\sum x)/(n)=(1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4)/(10)=2.65`

The number of terms is 10 which is an even number. So, the median of the data is

`Median=(((n)/(2))th+((n)/(2)+1)th)/(2)=(5th+6th)/(2)=(2.5+2.5)/(2)=2.5`

If next student presents a monologue that is about 0.5 minutes long, then the new data is

0.5, 1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4

The mean of the new data is

`Mean=(\sum x)/(n)=(0.5+1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4)/(11)=2.4545..\approx 2.45`

The number of terms is 11 which is an odd number. So, the median of the new data is

`Median=((n+1)/(2))th=6th=2.5`

Median of given data and new data is same but the mean of new data is less than the mean of original data. It means the mean will decrease.

Therefore the correct option is B.