Question

The mean of 5 observations \(x, x+2, x+4, x+6\) and \(x+8\), is 11, then the value of x is :

• A. 6
• B. 11
• C. 7
• D. 8

Hint:

1. Sum the observations: \(x + (x+2) + (x+4) + (x+6) + (x+8) = 5x + 20\). 2. Number of observations = 5. 3. Mean = (Sum of observations) / (Number of observations). 4. Set up the equation: \(11 = \frac{5x + 20}{5}\). 5. Solve for \(x\): \(55 = 5x + 20\) \(35 = 5x\) \(x = 7\).

Answer 1

The Correct Option is C

Concept: The mean (average) of a set of observations is calculated by summing all the observations and dividing by the number of observations. Step 1: List the given information Number of observations = 5 The observations are: \(x, x+2, x+4, x+6, x+8\) The mean of these observations = 11. Step 2: Write the formula for the mean Mean = \(\frac{\text{Sum of observations}}{\text{Number of observations}}\) Step 3: Calculate the sum of the observations Sum = \(x + (x+2) + (x+4) + (x+6) + (x+8)\) Combine the 'x' terms: \(x+x+x+x+x = 5x\) Combine the constant terms: \(2+4+6+8 = 20\) So, Sum = \(5x + 20\). Step 4: Set up the equation using the given mean We are given that the mean is 11. \[ 11 = \frac{5x + 20}{5} \] Step 5: Solve for x Multiply both sides by 5: \[ 11 \times 5 = 5x + 20 \] \[ 55 = 5x + 20 \] Subtract 20 from both sides: \[ 55 - 20 = 5x \] \[ 35 = 5x \] Divide by 5: \[ x = \frac{35}{5} \] \[ x = 7 \] The value of x is 7. Step 6: Verify the observations and mean (optional) If \(x=7\), the observations are: \(7, (7+2)=9, (7+4)=11, (7+6)=13, (7+8)=15\) Sum = \(7+9+11+13+15 = 55\) Mean = \(55 / 5 = 11\). This matches the given mean. The value of x is 7. This matches option (3).