Can standard deviation ever be negative ?
Last updated date: 28th Mar 2023
•
Total views: 206.7k
•
Views today: 5.89k
Answer
206.7k+ views
Hint:The standard deviation is a measure of amount of variation or dispersion of a set of values. In the given question, we have to find if the standard deviation of some observations can ever be negative.
Complete answer:
So, we have to check whether the standard deviation for a set of data or observations can be negative or not. The standard deviation of any set of observations can be minimum zero. Whenever, there are two unequal terms in the observations, the standard deviation is positive, that means greater than zero.
If all the observations are exactly equal, then the standard deviation is exactly zero.So, under no circumstances, the standard deviation can be negative or less than zero. We know that the standard deviation is the square root of variance of the observations. We also know that the square root of any quantity is always positive or zero.
Hence, the standard deviation is always non-negative.
Note:The given question revolves around the concepts of statistics. So, we should know the formulae for calculating the standard deviation and the properties that help to compute standard deviation of a given data set easily.
Complete answer:
So, we have to check whether the standard deviation for a set of data or observations can be negative or not. The standard deviation of any set of observations can be minimum zero. Whenever, there are two unequal terms in the observations, the standard deviation is positive, that means greater than zero.
If all the observations are exactly equal, then the standard deviation is exactly zero.So, under no circumstances, the standard deviation can be negative or less than zero. We know that the standard deviation is the square root of variance of the observations. We also know that the square root of any quantity is always positive or zero.
Hence, the standard deviation is always non-negative.
Note:The given question revolves around the concepts of statistics. So, we should know the formulae for calculating the standard deviation and the properties that help to compute standard deviation of a given data set easily.
Recently Updated Pages
Which element possesses the biggest atomic radii A class 11 chemistry JEE_Main

The highly efficient method of obtaining beryllium class 11 chemistry JEE_Main

Which of the following sulphates has the highest solubility class 11 chemistry JEE_Main

Amongst the metal Be Mg Ca and Sr of group 2 of the class 11 chemistry JEE_Main

Which of the following metals is present in the greencolored class 11 chemistry JEE_Main

To prevent magnesium from oxidation in the electrolytic class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE
