Question

There is a set of 100 observations with a mean of 40 and a standard deviation of 0. What is the value of the smallest observation in the set?

Answer 1

Answer with Step-by-step explanation:

There is a set of 100 observations with a mean of 40 and a standard deviation of 0.

standard deviation=0

means that variance=0     (since, variance=square of standard deviation)

now, variance is calculated as sum of the square of deviations of all the data points from the mean

i.e. if x1,x2,...xn are n observations, then

$\dfrac{(x1-mean)^2+(x2-mean)^2+...(xn-mean)^2}{n}$  is the variance

since variance is zero means that each of $(xi-mean)^2$ is zero

i.e. xi=mean for each i=1,2,...n

Hence here each of the observation is equal to mean=40

Hence, the value of the smallest observation in the set is:

      40

Answer 2

A standard deviation of 0 means that nothing deviates, in other words all observations are 40. So 40 is the smallest, the largest, all of that!