Calculating Variance, Mean, and Standard Deviation Of Grouped/Ungrouped Data

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