Question

What conclusion can be determined from the dot plot below?

A dot plot showing two dots above 2, three dots above 3 five dots above 4, three dots above 5, and two dots above 6.

A) The median of the data set is 3.
B) The mean of the data set is 3.
C) The range of the data set is 5.
D) The number of observations is 15.

Please give the correct answer, there will be consequences if you don't which include being reported

Answer 1

The correct option is D.

Explanation:

From the given figure it is clear that two dots above 2, three dots above 3 five dots above 4, three dots above 5, and two dots above 6. It means the data set is

2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6

Total number of observations = 15

Therefore option D is correct.

15 is an odd number, so the median of the data is

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

`Median=(((15+1)/(2))th)/(2)=8th`

The 8th term of the data is 4, therefore the median of the data is 4. Option A is incorrect.

The mean of the data is

`Mean=(\sum x)/(n)=(2+2+3+3+3+4+4+4+4+4+5+5+5+6+6)/(15)=(60)/(15)=4`

The mean of the data is 4. Option B is incorrect.

Range of the data is

`Range=Maximum-Minimum`

`Range=6-2=4`

Range of the data is 4. Option C is incorrect.