The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?

Step-by-step solution

Let the original observations be x₁, x₂, , x₁₀₀ . The original arithmetic mean is x = 50 . The new observations are given by y_i = x_i - 5 20 . Using the property of arithmetic mean, if each observation is subjected to a linear transformation y_i = a x_i + b , the new mean is y = a x + b . Therefore, the new mean is y = x - 5 20 . Substituting x = 50 , we get y = 50 - 5 20 = 45 20 = 2.25 . Answer: 2.25