We need to find the mean of the 2 data set. For data set A, we get
![\operatorname{mean}=(3\cdot25+3\cdot26+27+2\cdot28+29+30+2\cdot31+32+2\cdot33+34+3\cdot35)/(20)]()
which gives
![\operatorname{mean}=(594)/(20)=29.7]()
The mean fot data set B is
![\operatorname{mean}=(3\cdot25+4\cdot26+4\cdot27+2\cdot28+2\cdot29+30+2\cdot31+32+34)/(20)]()
which gives
![\operatorname{mean}=(559)/(20)=27.95]()
By means of these results, we can cancel out options 2 and 4.
Lets find the median for data set A. The median is the middle number in the sorted. For set A the median is between the 10th number and 11th number, that is, its between 29 and 30. Then the median is
![\operatorname{median}=(29+30)/(2)=29.5]()
Similarly, the median for data set B is between 10th number and 11th number, that is,
![\operatorname{median}=(27+27)/(2)=27]()
So, we can conclude for data set A that the mean and median are close in value because mean=29.7 and median=29.5. Which corresponds to option 6.
Now,
- option 1 is incorrect because data set B is skewed right.
- option 2 is incorrect because mean for A is 29.7 and for B is 27.95
- option 3 is incorrect because the values of set A are more spread than set B
- option 4 is incorrect for the same reason than option 2
- option 5 is correct for the same reason that option 3 and because the values for set B are more focalized around the mean.
- option 6 is correct because for data set A the mean and median are close in value: mean=29.7 and median=29.5