Question

What is the symbol for sample standard deviation ?

Answer 1

Hint: In this type of questions firstly we need to understand the term standard deviation by reading its definition and after understanding all the basic concepts and derivation of sample standard deviation we will get to know the symbol of sample standard deviation.

Complete step by step answer:
The standard deviation is a measure of the amount of variation or dispersion of a set of values. Standard deviation may be abbreviated SD. The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. There are two types of standard deviations: Sample standard deviation and population standard deviation.
The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population. While a sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since, the sample standard deviation depends upon the sample, it has greater variability.
A standard deviation is a measure of how dispersed the data is in the relation to the mean. Low standard deviation means data are clustered around the mean and the high standard deviation indicates data are more spread out.
Standard deviation is represented by the symbol $$\sigma$$ (known as Greek letter sigma).
The formula used for standard deviation is as:
$$\sigma =\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{(x_i-\mu )}^2}$$
Now as if we have to calculate the standard deviation of some numbers, then we have to follow some of these steps:
Find out the mean of all the given numbers (i.e. the simple average of all the numbers)
Then for each of the given numbers: subtract the mean and then square the result.
Then work out the mean of those squared differences (i.e. add up all of them and then divide by the total number of elements)
Now at last take the square root of that and you will get the standard deviation.
So our final answer is that the symbol for sample standard deviation is $$\sigma$$ .

Note: Standard deviation has its own advantages over any other measure of spread. The square of small numbers is smaller (Contraction effect) and large numbers larger (Expanding effect). So it makes you ignore small deviations and see the larger one clearly. The square is a nice function.