Find the median of 5,9,1,10,3,8,9,2,4,5,5,5,7,3 and 6

Analysis

To find the median of a set of numbers, you must first arrange them in ascending order (from the smallest to the largest). The median is the middle value in the ordered list.

Concept

If the total number of values ($n$) is odd, the median is the value at the position $\frac{n+1}{2}$. If $n$ is even, the median is the average of the two middle values.

Step-by-Step Solution

Step 1: List the given numbers 5, 9, 1, 10, 3, 8, 9, 2, 4, 5, 5, 5, 7, 3, 6

Step 2: Count the numbers There are 15 numbers in the set ($n = 15$). Since 15 is an odd number, there will be exactly one middle value.

Step 3: Arrange the numbers in ascending order 1, 2, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 9, 10

Step 4: Locate the middle position Using the formula $\frac{n+1}{2}$: $\frac{15 + 1}{2} = \frac{16}{2} = 8$ The median is the 8th number in the ordered list.

Step 5: Identify the 8th number 1st: 1 2nd: 2 3rd: 3 4th: 3 5th: 4 6th: 5 7th: 5 8th: 5 9th: 5 ...and so on.

The 8th number is 5.

Conclusion

The median of the set is 5.

Exam Tip

Always double-check your count before you start ordering the numbers. A common mistake in JAMB exams is skipping a number while rewriting the list. After you arrange them, count the original list and your new list to ensure you have the same number of items (in this case, 15).