Question

The double dot plot shows two data sets. The measure of the center of set A is how many times the measures of variation of set B?

• A. $\frac{34}{11}$
• B. $\frac{34}{15}$
• C. $\frac{34}{16}$
• D. $\frac{24}{25}$

Answer 1

The correct option is A $\frac{34}{11}$

Mean of data set A $=\frac{(1\times 1)+(2\times 2)+(3\times 4)+(4\times 3)+(5\times 1)}{(1+2+4+3+1)}=\frac{34}{11}$

Mean of data set B $=\frac{(1\times 4)+(2\times 4)+(3\times 4)+(4\times 4)}{4+4+4+4}=\frac{40}{16}=2.5$

MAD of set B $=\frac{(|1-2.5|\times 4)+(|2-2.5|\times 4)+(|3-2.5|\times 4)+(|4-2.5|\times 4)}{4+4+4+4}=\frac{6+2+2+6}{16}=\frac{16}{16}=1$

$\frac{\text{Mean of set A}}{\text{MAD of set B}}=\frac{\frac{34}{11}}{1}=\frac{34}{11}$

So, the measure of the center of set A is $\frac{34}{11}$ times the measure of variation of set B.