Question

What conclusion can be determined from the dot plot below? 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.

Answer 1

Given:

Consider the below figure attached with this question.

To find:

The conclusion that can be determined from the dot plot.

Solution:

The number of dots in the dot plot is 15. So, the number of observations is 15 and option D is correct.

The data set represented by the dot plot is:

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

Number of observations is 15, which is an odd number. So, the median of the data set is:

$Median=\dfrac{15+1}{2}\text{th term}$

$Median=\dfrac{16}{2}\text{th term}$

$Median=8\text{th term}$

$Median=4$

The median of the data set is 4. So, option A is incorrect.

Mean of the data set is:

$Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}$

$Mean=\dfrac{2+2+3+3+3+4+4+4+4+4+5+5+5+6+6}{15}$

$Mean=\dfrac{60}{15}$

$Mean=4$

The mean of the data set is 4. So, option B is incorrect.

The range of the data set is:

$Range = Maximum - Minimum$

$Range = 6-2$

$Range = 4$

The range of the data set is 4. So, option C is incorrect.

Therefore, the correct option is D.