Question

Calculate the median, the range and identify the Q1 and Q3 for the following set: 5, 1, 6, 8, 1, 7, 4, 5, 6, 11, 3, 4, 4, 2, 5, 5 (hint draw a box and whisker plot)

Answer 1

Arrange the data in ascending order

1,1,2,3,4,4,4,5,5,5,5,6,6,7,8,11

n=16

position of median = (n+1)/2 = 17/2 = 8.5 th item

8.5 th item is the average of 8 and 9th item

median = (5+5)/2 = 5

Range = largest value - smallest value

= 11 -1 = 10

position of Q1= (n+1)/4 = 17/4 = 4.25 th item

Q1 = 4 + 0.25(5th item - 4th item )

4 + 0.25(4-3)

= 4.25

position of Q3= (n+1)/4 = 3*17/4 = 12.75 th item

Q1 = 12 + 0.75(13th item - 12th item )

12 + 0.75(6-6)

= 12

Explanation: