Question

If the mean of a set of observations \( x_1, x_2, ..., x_{10} \) is 20, then the mean of \( x_1+4, x_2+8, x_3+12, ..., x_{10}+40 \) is

• A. \( 34 \)
• B. \( 32 \)
• C. \( 42 \)
• D. \( 38 \)
• E. \( 40 \)

Hint:

Adding different constants requires summing them separately.

Answer 1

The Correct Option is C

Concept: Mean shifts when constants are added to each term.

Step 1: Write original sum.
\[ \text{Mean} = 20 \Rightarrow \text{Sum} = 10 \times 20 = 200 \]

Step 2: Identify added sequence.
\[ 4,8,12,...,40 \]

Step 3: Find sum of added numbers.
This is AP: \[ n=10, a=4, d=4 \] \[ S = \frac{10}{2}(4+40) = 5 \times 44 = 220 \]

Step 4: New total sum.
\[ 200 + 220 = 420 \]

Step 5: Compute new mean.
\[ \frac{420}{10} = 42 \]