A data consists of 20 observations x₁, x₂, , x₂₀ . If _ i=1 ²⁰(x_i + 5)^2 = 2500 and _ i=1 ²⁰(x_i - 5)^2 = 100 , then the ratio of mean to standard deviation of this data is:

Step-by-step solution

Given _ i=1 ²⁰(x_i + 5)^2 = 2500 and _ i=1 ²⁰(x_i - 5)^2 = 100 . Expanding the first equation: _ i=1 ²⁰ (x_i^2 + 10x_i + 25) = 2500 _ i=1 ²⁰ x_i^2 + 10 _ i=1 ²⁰ x_i + 500 = 2500 _ i=1 ²⁰ x_i^2 + 10 _ i=1 ²⁰ x_i = 2000 --- (1) Expanding the second equation: _ i=1 ²⁰ (x_i^2 - 10x_i + 25) = 100 _ i=1 ²⁰ x_i^2 - 10 _ i=1 ²⁰ x_i + 500 = 100 _ i=1 ²⁰ x_i^2 - 10 _ i=1 ²⁰ x_i = -400 --- (2) Subtracting (2) from (1): 20 _ i=1 ²⁰ x_i = 2400 _ i=1 ²⁰ x_i = 120 Adding (1) and (2): 2 _ i=1 ²⁰ x_i^2 = 1600 _ i=1 ²⁰ x_i^2 = 800 M