Question

The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13^th observation is

• A. 30
• B. 29
• C. 28
• D. 31

Answer 1

The correct option is B

29

Let x₁,x₂, x₃ …….., x₁₂ be the 12 observations of the given data.

Let the 13^th observation be x₁₃.

x₁ + x₂ + x₃ ……..+ x₁₂ = 12 19.25 = 231 … (1)

x₁ + x₂ + x_{3 +}…….. + x₁₂ + x₁₃ = 13 20 = 260

(x₁ + x₂ + x_{3 +} …….. + x₁₂) + x₁₃ = 260

Using (1),

x₁₃ = 260 - 231 = 29