Multiple choice

The mean of two samples of sizes $200 $ and $300$ were found to be $25$ and $10$ respectively. Their standard deviations were $ 3 $ and $4$ respectively. The varience of combined sample size of $500$ is

  1. $64$
  2. $65.2$
  3. $67.2$
  4. $64.2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The combined variance is calculated using the formula for combined mean and variance. First, find the combined mean: (200*25 + 300*10) / 500 = 16. Then, use the formula: Variance = (n1(s1^2 + d1^2) + n2(s2^2 + d2^2)) / (n1 + n2), where d1 = 25-16 = 9 and d2 = 10-16 = -6. This yields (200*(9+81) + 300*(16+36)) / 500 = (18000 + 15600) / 500 = 33600 / 500 = 67.2.

AI explanation

Using the formula for the combined mean of two groups, M equals (n1 times m1 plus n2 times m2) divided by (n1 plus n2), which gives (200 times 25 plus 300 times 10) divided by 500, yielding a combined mean of 16. The combined variance is found using the formula sigma squared equals (n1 times (sd1 squared plus d1 squared) plus n2 times (sd2 squared plus d2 squared)) divided by (n1 plus n2), where d1 and d2 are the differences between the respective sample means and the combined mean. Plugging in the values gives (200 times (9 plus 81) plus 300 times (16 plus 36)) divided by 500, which simplifies to (18000 plus 15600) divided by 500, resulting in a combined variance of 67.2.

Keep practicing — related questions