If the mean of 2, 5, (x+1), (x+2), 7 and 9 is 6. Find the median

1. Analyze the question

We are given a set of six numbers: 2, 5, (x+1), (x+2), 7, and 9. We are told their mean is 6. We need to find the value of $x$ first, then arrange the numbers in order to determine the median.

2. Explain the concept

• Mean: The sum of all values divided by the total number of values. $$\text{Mean} = \frac{\sum x}{n}$$
• Median: The middle value of a data set when arranged in ascending or descending order. If there is an even number of values (like 6 here), the median is the average of the two middle terms.

3. Show the solution

Step 1: Find the value of $x$ The mean is 6, and there are 6 numbers.

Combine the constants:

So, the equation becomes:

Multiply both sides by 6:

Step 2: List the numbers Substitute $x = 5$ into the expressions:

• $x + 1 = 5 + 1 = 6$
• $x + 2 = 5 + 2 = 7$

The set of numbers is: 2, 5, 6, 7, 7, 9

Step 3: Find the median Since there are 6 numbers (an even number), the median is the average of the 3rd and 4th terms:

• 3rd term = 6
• 4th term = 7

4. Identify the answer

Comparing our result to the options provided, the correct option is C.

5. Tip

When finding the median of an even-numbered set, don't just pick the middle number—always remember to add the two central values and divide by 2. Also, always re-arrange your data in ascending order before looking for the median; if you had used the original order, you might have gotten the wrong answer!