The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?

Step-by-step solution

Let the original observations be x₁, x₂, , x₁₀₀ . The standard deviation of these observations is _x = 10 . The new observations are given by y_i = x_i + 5 20 = 1 20 x_i + 1 4 . If a new variable is defined as y_i = ax_i + b , its standard deviation is given by _y = |a| _x . Substituting a = 1 20 and _x = 10 : _y = | 1 20 | 10 = 0.5 The new standard deviation is 0.5 . Answer: 0.5