Which set of data has the smallest difference between the mean and the median? O A 13, 42, 17, 26, 38
OB. 28, 7, 36, 8, 17
OC 14, 29, 38, 7, 13
OD 23, 36, 25, 38, 30

D 23, 36, 25, 38, 30

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all it's values divided by the number of values.

Median of a data-set:

The median of a data-set is the value that separates the lower 50% from the upper 50% on the ordered set.

If the cardinality n is odd, as in this case, the median is the element at the position (n+1)/2. Since in this case, n = 5, the median is the 3rd element in the ordered set.

A 13, 42, 17, 26, 38

Ordered set: 13, 17, 26, 38, 42

Median: 26

Mean: (13+17+26+38+42)/5 = 27.2

Difference: 27.2 - 26 = 1.2

B. 28, 7, 36, 8, 17

Ordered set: 7, 8, 17, 28, 36

Median: 17

Mean: (7+8+17+28+36)/5 = 19.2

Difference: 19.2 - 17 = 2.2

C 14, 29, 38, 7, 13

Ordered set: 7, 13, 14, 29, 38

Median: 14

Mean: (7+13+14+29+38)/5 = 20.2

Difference: 20.2 - 14 = 6.2

D 23, 36, 25, 38, 30

Ordered set: 23, 25, 30, 36, 38

Median: 30

Mean: (23+25+30+36+38)/5 = 30.4

Difference: 30.4 - 30 = 0.4

Option d has the smallest difference.