Question

•Set A has eight different data values in it; they are all between 180 and 200

•Set B has nine different data vlaues in it: All the sams data values as Set A along with an additional data value of 0.

A)which set has higher mean?

B)which set has higher median?

C)which set has higher standard deviation?

Answer 1

A. Set A has higher mean, because mean=sum of data values/ number of data values

here extra data in set B is zero, but sample size of B is high, so the denominator in the mean of set B is high, which leads to mean value lesser than set A.

B. Set A has a higher median, because in median data should be arranged in ascending order, so 0 data value will come to first in set B and since the sample size of B is 9 that is odd so middle number is needed to be picked, but in set A sample size is 8 so mean of 2 middle values need to be taken, so mean will be more.

C. Set B has more standard deviation, because in standard deviation formula, one data value od set B is zero but (0-mean) value will add up in the numerator, which leads to more standard deviation that set A.