Chapter Name : Statistics |
Sub Topic Code : 104_11_15_05_03 |
Topic Name : Variance And Standard Deviation |
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Sub Topic Name : Standard Deviation Of A Discrete Frequency Distribution |
• 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 discrete frequency distribution is a measure of dispersion used in interpreting data sets.
• Knowledge of measure of dispersion. • Knowledge of mean, median of data.
You will observe that standard deviation is helpful in knowing which heights are within standard deviation of mean.
How does your teacher come to know what teaching strategies are required to teach students based on marks scored?
Key Words | Definitions (pref. in our own words) |
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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. |
Discrete frequency distribution | Given data with n observations have respective frequencies. Example : x 10 6 12 7 8 14 f 5 4 7 2 3 1 |
Gadgets | How it can be used |
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Graph paper | Take measurements of heights of your friends. Find the mean, variance and standard deviation. Plot heights on graph paper. |
Standard deviation is used in sports, finance, weather forecasting, in knowing normal heights, weights of population.
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.
Examples | Explainations |
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Measure of standard deviation in weather forecasting. | Weather department considers the average maximum temperature for two cities one inland and one on coast. While two cities may have same average maximum temperature, the standard deviation of the daily maximum temperature for the coastal city will be less than that of inland city. |
Standard deviation is square root of variance.
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.
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