Question

What happens to the mean of the data set {10, 2, 8, 9, 5, 2, 6} if the number 9 is removed from the data set?

Answer 1

If we remove 9 from the data set, the mean reduces by 0.5 from 6 to 5.5

Explanation:

• Mean of {10, 2, 8, 9, 5, 2, 6}}
  = (10 + 2 + 8 + 9 + 5 + 2 + 6)/7
  = 42/7
  = 6

• If 9 is removed from the data set, the total reduces from 42 by 9
  42 - 9 = 33

• The number of elements reduces by 1:
  7 - 1 = 6

• The new mean
  = 33/6
  = 5.5

Answer
If we remove 9 from the data set, the mean reduces by 0.5 from 6 to 5.5