Question

A data set has the following six data points: 11, 3, x, x+2, 5, 10. If the median if this data set is 7, then what is the possible value of x?

Answer 1

x=6

Explanation:

• The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers

11, 3, x, x+2, 5, 10

in ascending order the data points:

• 3, 5, 10, 11, x, x+2, then median >7
• x, x+2, 3, 5, 10, 11 then median <7
• 3, 5, x, x+2, 10, 11 then median is (x+x+2)/2=7 ⇒ x+1=7 ⇒ x=6