Question

Question 5 of 10There is a set of 100 observations with a mean of 40 and a standarddeviation of o. What is the value of the smallest observation in the set?A. 70B. 20D. 40SER

Answer 1

The standard deviation can be calculated using the formula:

`\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N-1}}`

Where N is the number of observations, x_i is each observation and μ is the mean. From that, we can see that, for the standard deviation be zero,

`(x_i-\mu)^2=0`

For all observations. This meas that all of the 100 observations must be the same value and equal to the mean:

`\begin{gathered} (x_i-\mu)^2=0 \\ x_i-\mu=0 \\ x_i=\mu=40 \end{gathered}`

If all observations are equal to 40, so is the smallest observations. So, the smallest observation must be equal to 40, which is alternative D.