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Introduction
We will learn how to calculate the mean, variance, and standard deviation of grouped and ungrouped data. The variance calculator can be used to calculate the variance, standard deviation, and mean from a set of data with the sample size n to understand how far the observations deviate from the mean. The deviations can be either positive or negative. We must square the values to prevent positive and negative values from cancelling each other when we add up all the deviations.
Types of Data
Data is defined as the collection of facts or information from which conclusions can be drawn. The collected information can be numbers, words, measurements, and more.
There are several ways to classify data. One way to classify data is in terms of grouped data and ungrouped data.
Ungrouped Data
Ungrouped data is data that is not segregated into categories. It is also known as raw as it is not aggregated.
Example 1: Height of students
(177, 144, 151, 175, 166, 142, 163, 170, 161, 172, 162, 158, 190, 151, 187, 151, 160, 177, 148, 164)
Grouped Data
Data is referred to as grouped data when the raw data is organised into categories.
Example 2: Height of students in a table
How to calculate mean for grouped data?
To calculate the mean for grouped data, we will use the data from Example 2: Height of students given in a tabular form below and calculate the midpoints of the intervals. The sum of observations is calculated by multiplying the frequency with the midpoint of the interval.
Variance
What is variance?
The variance is an estimate of the degree of variability. It is determined by averaging the square of deviations from the mean. The degree of dispersion in the data is indicated by the variance calculator. The wider the data spread, the higher the variance from the mean.
How to calculate variance for ungrouped data?
