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Standard Deviation

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Standard Deviation

Variation (dispersion) is the property of deviation of values from the average. The degree of variation is indicated by the measures of variation. There are various measures of variation and the commonly used ones are:
1.Range
2.Mean deviation
3.Standard Deviation
4.Quartile deviation.

The standard deviation of a set of values is the positive square root of the mean of the standard deviations of the values from their arithmetic mean. It is denoted by s (sigma). The measures of dispersion are statistical devices to measure the variability or the dispersion in a series. The Measures of Central tendency are the average of the original values. So, they are known as the averages of the first order. The measures of dispersion are only averages of deviations taken from the average. Therefore, they are known as the averages of the second order.

Standard Deviation Definition

Standard Deviation is a measure of dispersion in statistics. It gives an idea of how the individual data in a data set is dispersed from the mean. Standard deviation is defined as the square root of the mean of the squares of the deviations of all the values of a series taken from the arithmetic mean. It is also known as the root mean square deviation. The symbol used for standard deviation is s.

1. The minimum value of standard deviation is 0. i.e. it cannot be negative.
2. When the items in a series are more dispersed from the mean, then the standard deviation is also large.

Purpose of Standard Deviation
The purpose of obtaining the standard deviation is to measure the standard distance from the mean.

Merits of standard deviation

It is based on all observations in a distribution.
It is capable of further algebraic treatment.
We can find out measures like coefficient of variation, combined standard deviation extra.

Demerits of Standard deviation

It is difficult to calculate.
It gives more importance to bigger values.

Standard Deviation Unit
Standard deviation have the same units as the original data measurements.

Standard Deviation Symbol
"s" is used to show the standard deviation notation.

Symbol = s, s read as sigma.
or sx = Standard deviation value of random variable x.

Negative Standard Deviation
Standard deviation is the square root of a non-negative number. Standard deviation can be zero, but never negative. Both sides of the distribution result in positive value for standard deviation.

Variance and Standard Deviation

The variance and standard deviation are closely-related to each other, both are measures of variability. The variance is the average of the squared differences from the Mean and square root of the Variance is standard deviation.

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Standard Deviation Measures

We can measure the standard deviation by finding the variance. Given below are the steps to be followed for solving the problem.

Steps for Finding the Standard Deviation from the Variance:

Step 1: Calculate arithmetic mean of the list of numbers.

Step 2: We subtract the mean value from all the numbers in the list.

Step 3: In order to avoid the negative numbers from the part of calculation, square the negative numbers.

Step 4: Add the squared differences to get a single number.

Step 5: Now find the variance to get the standard deviation.

Step 6: From the variance we can find the standard deviation by finding the variancevvariance.
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