Question

If the mean of 5 observations x, x+2, x+4, x+6 and x+8 is 11, then value of x

• A. 7
• B. 43
• C. 51
• D. 8

Answer 1

The Correct Option is A

To find the value of \(x\), we start by using the formula for the mean of a set of observations. The mean of the 5 observations \(x, x+2, x+4, x+6, x+8\) is given as 11.
Step 1: First, write down the expression for the sum of the observations:
\[x+(x+2)+(x+4)+(x+6)+(x+8)\]
Step 2: Simplify the sum:
\[5x+20\]
Step 3: Use the formula for the mean, which is the sum of observations divided by the number of observations:
\[\text{Mean} = \frac{5x+20}{5} = 11\]
Step 4: Solve the equation for \(x\):
\[\frac{5x+20}{5} = 11\]
Multiply both sides by 5:
\[5x+20 = 55\]
Step 5: Subtract 20 from both sides:
\[5x = 35\]
Step 6: Divide both sides by 5:
\[x = 7\]
Thus, the value of \(x\) is 7.