Question

One of the concepts that is key to understanding statistics is standard deviation. Standard Deviation is a measurement of how varied or similar your data is - so if you have outliers, this will mean that you will have a larger standard deviation.

Standard deviation is the square root of the variance.

The variance (σ2) is a measure of how far each value in the data set is from the mean. Here is how it is defined:

1.   Subtract the mean from each value in the data. This gives you a measure of the distance of each value from the mean.

2.   Square each of these distances (so that they are all positive values), and add all of the squares together.

3.   Divide the sum of the squares by the number of values in the data set.

The standard deviation (σ) is simply the (positive) square root of the variance.

How can this be put to practical use?

Answer 1

Use:- 1) If data is given and you have to check varaition or deviation that means spreadness or dispersion of data ie how data is varying from mean then use variance. Eg. If you have share price of any company, then is variance is greater then it indicates that price up-down is large , where risk and profit is available.

2) while fitting regression model , to check data fits to model with adequately.

E.g. supposed linear model first we checked the spreadsheet for the data using standard we get idea about how much data dispersed, if more then model is not convenient to use.

Practical use:- for given question,

Take a data from SRS with n number of sample.

Or you can conduct experiment using dice.

Notedown the values then find variance and s.d using given step

You will observed that s.d is square root of variance.