187k views
4 votes
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?

2 Answers

3 votes
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!
User Paulo Griiettner
by
7.7k points
0 votes

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


((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

User Sander Visser
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories