Question

What conclusion can be derived by comparing the central tendencies of the two data sets?

1: {7, 6, 3, 1, 6, 2, 4, 6, 3, 5}
2: {2, 2, 2, 3, 4, 5, 2, 8, 7, 6}

A.The mean of set A is smaller than the mean of set B

B.The median of set A is greater than the median of set B.

C.The median and the mean of set B are greater than those of set A.

D.The mode of set B is greater than the mode of set A.

Answer 1

Arranging the set 1 in ascending order we have:

Set 1={1, 2, 3, 3, 4, 5, 6, 6, 6, 7}

Mean = Sum of the number ÷ Total numbers = (1 + 2 + 3 + 3 + 4 + 5 + 6 + 6+6 + 7) ÷10 = 43÷10=4.3

Median = (4+5)÷2= 4.5

Mode = 6

Set 2 :

Arranging in ascending order :

Set 2 ={2, 2, 2, 2, 3, 4, 5, 6, 7, 8}

Mean =(2 + 2 + 2 + 2 + 3 + 4 + 5 + 6 + 7 + 8) ÷10=41÷10= 4.1

Median =(3+4)÷2 =7÷2=3.5

Mode = 2.

Among the options given we see:

B.The median of set A is greater than the median of set B is the right option.