Variance And Standard Deviation
Chapter Name : Statistics |
Sub Topic Code : 104_11_15_05_05 |
Topic Name : Variance And Standard Deviation |
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Sub Topic Name : Shortcut Method To Find Variance And Standard Deviation |
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Introduction
• Statistics deals with data collected for specific purposes. • In order to have better data interpretation we should know how data is scattered and this measure is known as Measure of Dispersion. • Variance and standard deviation are measures of dispersion. • Shortcut method to find variance and standard deviation is called as Step Deviation method.
Pre-Requisites:
• Knowledge of measure of dispersion. • Knowledge of Variance, Standard deviation.
Activity:
You will observe that friend having low standard deviation of marks is a consistent performer. You can observe easily by plotting points on graph.
Real Life Question:
A shopkeeper wants to compare sales of two products over a period of one year. Use standard deviation to find which product varied the most in its monthly sales.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Statistics | Statistics is a method of gathering, analyzing and making conclusions from data. |
| Standard deviation | Standard deviation is a measure of dispersion and it helps to look at a set of data and make assumptions. The bigger the standard deviation the more data is spread out, the smaller standard deviation there is less variation in data. |
| Step Deviation Method | Sometimes values of midpoints in various class intervals are large and calculating mean and variance becomes time consuming. For this reason we have a short cut method for calculating variance called as Step Deviation Method. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graph paper | Collect marks of different subjects of your friends such that they have same average. Plot marks on graph paper. Can you find out who is better? You can get the answer by using Standard deviation. You can find standard deviation using step deviation method. |
Real life uses :
Standard deviation is used in sports, finance, weather forecasting, in knowing normal heights, weights of population.
Places to visit :
Make data on money spend on number of household members for a month. Calculate standard deviation. By calculating standard variation you can know the variance of expenditures on number of household members.
Practical examples around us
| Examples | Explainations |
|---|---|
| Step deviation in scientific study. | In scientific study, standard deviation of data can indicate whether the data was consistent and therefore can help scientists in making scientific conclusions based on their data. If data is large then step deviation method is used to simplify calculations. |
What you learn in Theory:
Calculation in step deviation method is reduced for calculation of product values and their respective frequencies.
What you learn in Practice:
Step deviation simplifies calculations.