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Andrej [43]
3 years ago
11

Ms Redmond gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The gra

ph shows the times, rounded to the nearest half minute, of the first 10 monologues presented

Mathematics
2 answers:
ratelena [41]3 years ago
6 0

Answer:

The mean will decrease.

Radda [10]3 years ago
6 0

Answer:

The correct option is B.

Step-by-step 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=\frac{\sum x}{n}=\frac{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=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{5th+6th}{2}=\frac{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=\frac{\sum x}{n}=\frac{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=(\frac{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.

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