Problem Solving

Which of the following distribution of numbers has the greatest standard deviation?

(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}

I'm confused between A and D. Can any experts help?

Hello.

Let's take a look at your question.

We first need to calculate the mean value of each set of numbers:

$$M_A=0;\ M_B=0;\ M_C=5;\ M_D=2;\ M_E=2.$$

Now, we have to calculate the standard deviation of each set of numbers:

$$SD_A=\sqrt{7};\ SD_B=\sqrt{\frac{10}{3}};\ SD_C=2;\ SD_D=\sqrt{\frac{14}{3}}\ and\ SD_E=\ 2.$$

So, set A has the greatest standard deviation.

The correct option is A.

You can discard option D because $$7>14/3,\ so\ \sqrt{7}>\sqrt{\frac{14}{3}}.$$

I hope this explanation can help you.

Let me know if you have another doubt.

I'm available if you'd like a follow up.