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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:
[tex]Median=\dfrac{15+1}{2}\text{th term}[/tex]
[tex]Median=\dfrac{16}{2}\text{th term}[/tex]
[tex]Median=8\text{th term}[/tex]
[tex]Median=4[/tex]
The median of the data set is 4. So, option A is incorrect.
Mean of the data set is:
[tex]Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
[tex]Mean=\dfrac{2+2+3+3+3+4+4+4+4+4+5+5+5+6+6}{15}[/tex]
[tex]Mean=\dfrac{60}{15}[/tex]
[tex]Mean=4[/tex]
The mean of the data set is 4. So, option B is incorrect.
The range of the data set is:
[tex]Range = Maximum - Minimum[/tex]
[tex]Range = 6-2[/tex]
[tex]Range = 4[/tex]
The range of the data set is 4. So, option C is incorrect.
Therefore, the correct option is D.
