Variance And Standard Deviation
Chapter Name : Statistics |
Sub Topic Code : 104_11_15_05_01 |
Topic Name : Variance And Standard Deviation |
|
Sub Topic Name : Variance And Standard Deviation |
|
Introduction
• Statistics deals with data collected for specific purposes. • To measure how spread out data is we need to have a measure called variance. It is average of squared difference from mean.
Pre-Requisites:
• Knowledge of representing data graphically and in tabular form. • Knowledge of measure of dispersion.
Activity:
You will observe that taking squared difference leads to proper measure of dispersion.
Real Life Question:
Find the variance in runs scored by batsman in 5 matches. The scores are: 67,72,93.85,98.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Statistics | Statistics is a method of gathering, analyzing and making conclusions from data. |
| Variance | Variance is the measure of how spread out data is. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graph paper | Plot the points of set A (4,4,-4,-4) and set B(7,1,-6,-2). Find the mean. For each number subtract the mean and square the difference. Why is it required to square the difference? |
Real life uses :
Variance has applications in finance, sports, weather, depicting population height, weight charts.
Places to visit :
Take 6 tomatoes and measure diameter. The diameter of 6 tomatoes is your data set. Find the mean and variance of tomatoes.
Practical examples around us
| Examples | Explainations |
|---|---|
| Population height and weight. | Concept of variance is used in depicting population height and weight charts. Variance shows how spread out data is from mean of population. |
What you learn in Theory:
Variance is average of squared difference from mean.
What you learn in Practice:
Variance is common measure of dispersion. Even though the mean, minimum, maximum values of data is equal the variance shows different spread of data.