Use of Sample Variance Formula-Use, Application & Solved Questions

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About Sample Variance

The variability in a sample is calculated using sample variance. A sample is a collection of observations drawn from a population that can fully reflect it. The sample variance is calculated in relation to the data set's mean. The estimated variance is another name for it.

Because there are two forms of data, grouped and ungrouped, there are two formulas for calculating sample variance. Furthermore, the sample standard deviation is equal to the square root of the sample variance.

The spread of data points in a particular data set around the mean is measured using sample variance. The population refers to all of a group's observations. When the number of observations grows, calculating the population variance gets more complicated. In this case, small number of observations are chosen that can be utilised to describe the entire group. This particular set of data constitutes a sample, and the variance determined in this manner is the sample variance.

Sample Variance Definition

The expectation of the squared difference of data points from the data set mean is known as sample variance. It's an absolute measure of dispersion that's used to assess how far apart data points are from the average.

**Sample Variance Formula**
Data Categories	Sample Variance
Ungrouped Data	$\frac{\sum_{i = 1}^{n} {(x_{i} - μ)}^{2}}{n - 1}$
Grouped Data	$\frac{\sum_{i = 1}^{n} f {(m_{i} - \bar{x})}^{2}}{N - 1}$

Data can be divided into two categories: grouped and ungrouped. Ungrouped data is data that is in a disorganised and raw state. Grounded data is data that has been categorised into groups, categories, or tables. For both forms of data, the sample variance calculations are as follows:

Ungrouped Data: s² = $\frac{\sum_{i = 1}^{n} {(x_{i} - μ)}^{2}}{n - 1}$
Grouped Data: s² = $\frac{\sum_{i = 1}^{n} f {(m_{i} - \bar{x})}^{2}}{N - 1}$
n = total number of observations.
$N = {\sum f i}_{i = 1}^{n}$
f = frequency of occurrence of observation for the grouped data
mi = Mid-point of the i^thinterval

Mean for grouped data, x? = $\frac{{\sum m i f i}_{i = 1}^{n}}{{\sum f i}_{i = 1}^{n}}$

Mean for ungrouped data, μ = $\frac{{\sum x i}_{i = 1}^{n}}{n}$

Sample variance, on average, is equal to population variance.

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Sample Variance

About Sample Variance

Sample Variance Definition

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