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Sample Statistics

In statistics, sample and population are two very important terms. They have a whole different meaning in statistics. Population is the whole set of interests (people, places, objects etc) from which the data can be collected for a statistical research. On the other hand, sample is a part of population (since it is very big) and represents the whole population. Instead of collecting data from whole population, it is collected from its sample.

The part of statistics that is performed on samples is known as sample statistics.
 In other words, the calculation of statistical parameters on a sample is referred as its sample statistics.

Following important terminologies are frequently used is sample statistics :

Sample Mean

Sample mean is defined as average of the given sample.

The formula for sample mean (ungrouped data) is given below:

$\bar{x}=\frac{\sum x_{i}}{n}$
Where,
$\bar{x}$ = Sample mean
n = Total number of terms
$\sum x_{i}$ = Sum of all the observations in given sample.

Sample Median
Sample median is the middle most value of a sample when the data is arranged in ascending order.

Median of a sample is calculated by the following formulas:

1) If n (number of terms) is odd:
Sample Median =  $(\frac{n+1}{2})^{th}$ term

2) If n is even:
Sample Median = Average of $(\frac{n}{2})^{th}$ term and $(\frac{n}{2}+1)^{th}$ term
Sample Mode
Mode of a sample is calculated as the term which has highest frequency among all observations.

Sample Standard Deviation
Sample standard deviation is the measurement of deviation of each value in a sample from its mean.
 It is calculated by the following formula:
S = $\sqrt{\frac{\sum(x_{i}- \bar{x})}{n-1}}$
Where,
S = Sample standard deviation
n = Total number of observations
$ \bar{x}$ = Sample mean

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