Question

The following observations have been arranged in ascending order. If the median of the data is 22, then find the value of the 6th observation.

12,14,16,18,x-1, x+3,30,32,35,41

Answer 1

Answer: 24

Explanation:

The median is the middle number of the set. If the set contains an even number of terms, then the median is the average of the two middle numbers.

{12, 14, 16, 18, x-1, x+3, 30, 32, 35, 41}

Cross out the end terms to find the median: {X, X, X, X, x-1, x+3, X, X, X, X}

The median is the average of the two middle numbers (x-1 and x+3).

`((x-1)+(x+3))/(2)=22\\\\(x-1)+(x+3)=44\\\\2x+2=44\\2x=42\\x=21`

The 6th term is x+3 ⇒ 21 + 3 = 24