Multiple choice

The mean and standard deviations of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to

  1. 10

  2. 36

  3. 43

  4. 60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original sum of 50 observations = 50 * 15 = 750. The incorrect observation was replaced. Let the incorrect be x and correct be y. Given x + y = 70. New sum = 750 - x + y = 50 * 16 = 800. Solving x + y = 70 and y - x = 50 gives y = 60, x = 10. The new variance is calculated using the new sum of squares.

Keep practicing — related questions