Question

The mean of twenty observations x₁, x₂, x₃, x₄, ... x₂₀ is m. If each of the first ten observations is increased by 8 and each of the next 10 observations is decreased by 8, then the new mean is n. The difference m – n equals

(a) 16

(b) 20

(c) 0

(d) 8

Answer 1

Correct option is (c) 0

Mean is the sum of the data values divided by the total number of data values.

Given that mean of 20 observations x_1​, x₂​, ..., x₂₀​ is m

⇒ \(m = \frac{x_1 +x_2 + x_3 + ....+ x_{20}}{20}\)    .....(1) 

New mean after increasing first ten numbers by 8 and decreasing next ten numbers by 8 is n

Answer 2

The arithmetic mean, arithmetic average, is the sum of a collection of numbers divided by the count of numbers in the collection. Since by decreasing the same amount from the last ten observations as was added to the first ten observations, the sum total would not change and consequently the mean would not change and therefore the difference between the "old" mean and the "new" mean would be: (c) 0