Multiple choice

If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

  1. 16

  2. 6

  3. 5

  4. 4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Variance = (Sum of squares / n) - (Mean)^2. Variance = (16160 / 10) - 40^2 = 1616 - 1600 = 16. Standard deviation = sqrt(16) = 4.

AI explanation

Using the variance formula, the variance is calculated as the sum of squares divided by the number of observations minus the square of the mean. Plugging in the given values, we get 16160 divided by 10 minus 40 squared, which simplifies to 1616 minus 1600, giving a variance of 16. The standard deviation is the square root of the variance, so the square root of 16 is 4.

Keep practicing — related questions