Variance And Standard Deviation
Chapter Name : Statistics |
Sub Topic Code : 104_11_15_05_04 |
Topic Name : Variance And Standard Deviation |
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Sub Topic Name : Standard Deviation Of A Continuous Frequency Distribution |
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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. • Standard deviation of continuous frequency distribution is a measure of dispersion used in interpreting data sets.
Pre-Requisites:
• Knowledge of measure of dispersion. • Knowledge of mean, median of data.
Activity:
You will observe that standard deviation is helpful in knowing which weights are within standard deviation of mean.
Real Life Question:
World Health Organization expert committee obtained data with regard to weights of people according to geographic locations. How will they know the variations in weights of people?
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. |
| Continuous frequency distribution | Given data is in the form of class intervals without any gaps with their respective frequencies. Example : x 10-20 20-30 30-40 f 5 4 7 |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graph paper | Take measurements of weights of your friends. Find the mean, variance and standard deviation. Plot weights on graph paper. |
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 |
|---|---|
| Standard 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. |
What you learn in Theory:
Standard deviation is square root of the average of squared differences from mean. In continuous frequency distribution, midpoints of class intervals are calculated.
What you learn in Practice:
The larger the deviation, the more data is spread out, the lesser the deviation the variation is less in data. For example in racing car, the driver with low standard deviation of lap times is more consistent than driver with higher standard deviation.