If the mean of 4, y, 8 and 10 is 7. Find Y?

Analysis

To find the value of an unknown variable in a set of numbers when the mean is given, we use the definition of the arithmetic mean. The mean is the sum of all values divided by the total number of values.

Concept

The formula for the mean ($\bar{x}$) is:

In this problem:

• The values are: 4, $y$, 8, and 10.
• The number of values ($n$) is 4.
• The mean is 7.

Step-by-Step Solution

1. Set up the equation: $$\frac{4 + y + 8 + 10}{4} = 7$$

2. Simplify the numerator: Add the known numbers: $4 + 8 + 10 = 22$. So, the equation becomes: $$\frac{22 + y}{4} = 7$$

3. Clear the fraction: Multiply both sides by 4 to isolate the numerator: $$22 + y = 7 \times 4$$ $$22 + y = 28$$

4. Solve for $y$: Subtract 22 from both sides: $$y = 28 - 22$$ $$y = 6$$

Conclusion

The value of $y$ is 6.

Exam Tip

When dealing with mean questions, a quick way to check your work is to multiply the mean by the number of items to get the "Total Sum." Here, $7 \times 4 = 28$. Then, subtract the sum of the known numbers ($4 + 8 + 10 = 22$) from the total sum ($28 - 22 = 6$). This is a faster way to solve it during the actual JAMB exam!