A standard deviation is determined by taking the square root of what?

Question

BlackTom AI · Accepted Answer

The question asks: A standard deviation is determined by taking the square root of what?
Option 1: Median. Using the median has nothing to do with the spread of data; it is a measure of central tendency, not a dispersion measure. Therefore, this choice is incorrect.
Option 2: Average. While averages (means) relate to central tendency as well, standard deviation is not computed from the mean itself. It involves squared deviations from the mean, but the square root is applied to the variance, not to the mean directly. Thus, this option is not right.
Option 3: Variance. This is the correct concept: the standard deviation is the square root of the variance, which is the average of the squared deviations from the mean. The square root converts the squared units back to the original units of the data.
Option 4: Mean. The mean is a measure of central tendency, not a direct component in computing the standard deviation. Although the squared deviations are relative to the mean, the standard deviation is obtained by taking the square root of the variance, which requires averaging those squared differences first; the mean itself is not the quantity being square-rooted. Hence, this option is incorrect.

A standard deviation is determined by taking the square root of what? Single choice

Similar Questions

What’s the variance of a random variable X where E(X) = 0 ?

Which dataset below shows the greatest variance?

For some value of q, the expected value of X is 2.09, and the expected value of X^2 is 5.67 What is the variance of X?

If p = 0.6, what is the variance of the difference? (Hint: Let D=X-Y, where we let X represent the number of Facebook friend requests, and let Y represent the number of LinkedIn connection requests. What are the possible values for X and Y, as well as D? What are their probabilities?)

For this problem, what is the most appropriate unit for the variance for the number of friend requests? (Select the best answer.)

Suppose we do not know the exact value of p. However, we are given that the expected number of friend requests is 1.75, and the expected number of the square of friend requests is 3.95. What is the variance of the number of friend requests per day? (Hint: Which formula for variance is helpful here?)

Which dataset below shows the greatest variance?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler