The variance of 20 observations is 5. If each observation is multiplied by 3 and then 8 is added to each…
The variance of 20 observations is 5. If each observation is multiplied by 3 and then 8 is added to each number, then variance of resulting observations is
35
55
25
45
Solution
- Variance Calculation:
- Given: Variance $=5$ for 20 observations.
- Each observation is multiplied by 3: Variance gets multiplied by $3^2=$
- New variance:
$\text {New variance }=9 \times 5=45$
- Adding 8 to each observation does not change the variance.
- Final variance: 45. Answer: 45, which matches the solution shown.