Question

The mean of a data set with 10 observations is calculated as 17.85. If one more value is included in the data, then for the new data with 11 observations, mean becomes 18.50. Value of this 11^th observation is

• A. 24
• B. 28
• C. 25
• D. 26

Answer 1

The correct option is C

25

Let x₁, x₂, x₃ …, x₁₀ be the 10 values of the given data.

Let the 11^th observation be x₁₁.

x₁ + x₂ + x₃ + ……..+ x₁₀ = 10 17.85 = 178.5

x₁ + x₂ + x₃ + ……..+ x₁₀ + x₁₁= 11 18.50 = 203.50

(x₁ + x₂ + x₃ +……..+ x₁₀) + x₁₁ = 203.50

x₁₁ = 203.50 - 178.50 = 25