Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

To find the median of a set of numbers, follow these steps:

1. Analyze the question

The median is the middle value of a data set when the numbers are arranged in order of magnitude (either ascending or descending). Since there are 10 numbers in this set (an even number), the median will be the average of the two middle terms.

2. Explain the concept

• Step 1: Arrange the numbers in ascending order (from smallest to largest).
• Step 2: Identify the middle position. For $n$ numbers, if $n$ is even, the median is the average of the $(\frac{n}{2})^{th}$ and the $(\frac{n}{2} + 1)^{th}$ terms.
• Step 3: Calculate the average of those two middle terms.

3. Show the solution

Step 1: Arrange the numbers in ascending order: Original list: 89, 141, 130, 161, 120, 131, 131, 100, 108, 119

Ordered list:

1. 89
2. 100
3. 108
4. 119
5. 120
6. 130
7. 131
8. 131
9. 141
10. 161

Step 2: Identify the middle terms: Since there are 10 numbers ($n=10$), the middle terms are the 5th and 6th positions:

• 5th term = 120
• 6th term = 130

Step 3: Calculate the average:

4. Identify the answer

Comparing our result to the given options, the correct answer is B.

5. Exam Tip

Always count the number of items in your list before you start. If you have an odd number of items, the median is just the single middle number. If you have an even number of items, never forget to divide the sum of the two middle numbers by 2! A common mistake is to just pick one of the two middle numbers.