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Find a counterexample for the following statement. The standard deviation of a set of data is always less than the variance.

See explanation, answers can vary

Intro Stats / AP Statistics

Algebra

Chapter 12

Probability and Statistics

Section 6

Statistical Measures

Sampling and Data

The Normal Distribution

Introduction to Combinatorics and Probability

Oregon State University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:01

Give a sample set of data …

02:10

A set of data is normally …

00:30

What is the relationship b…

01:12

How is the standard deviat…

07:55

Provide an example that sh…

00:37

The sets of data for two d…

07:42

Find the variance and stan…

01:10

What are all the values th…

04:14

04:43

already. So for number 35 we are asked to figure out, um, a way to disprove the standard deviation is always bigger than the variance. Well, if we think back to just the previous problem and number 34 we were able to figure out that it is possible for the standard deviation and the various two equals zero. So if they each equal zero zero, is not, ah, bigger than zero, that is a false statement. So that would be an example there. Now there's plenty others. This is one of those answers. May very situations it if you find a decimal. Usually it's a number that's less than one, um, as your ah center deviation, you take the square root of it. Sometimes your variants will be bigger. So, um, that will also be the case is well

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