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# Standard deviation

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Standard deviation
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# Standard deviation

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### Standard deviation

1. 1. STANDARD DEVIATION SUBMITTED TO: NANCY
2. 2. TABLE OF CONTENTS ° WHAT IS STANDARD DEVIATION? ° METHODS OF CALCULATING STANDARD DEVIATION ° OBJECTIVE OF STANDARD DEVIATION ° MERITS AND DEMERITS OF STANDARD DEVIATION 2022 Standard deviation 2 ° STANDARD DEVIATION FORMULA ° INTRODUCTION
3. 3. SUMMARY MEASURES SUMMARY MEASURES CENTRAL TENDENCY VARIATION RANGE 2022 STANDARD DEVIATION 3 MEAN MODE MEDIAN QUARTILE DEVIATION STANDARD DEVIATION MEAN DEVIATION
4. 4. INTRODUCTION  While looking at the earlier measures of dispersion all of them suffer from one or the other demerit i.e,  RANGE: it suffer from a serious drawback considers only 2 values and neglect all the other value of the series.  QUARTILE DEVIATION: considers only 50% of the item and ignores the other 50% of the items in the series.  MEAN DEVIATION: no doubt an improved measure but ignores negative signs without any basis 2022 STANDARD DEVIATION 4
5. 5. WHAT IS STANDARD DEVIATION?  The concept of standard deviation was first introduced by karl Pearson in 1893.  Karl Pearson after observing all these things has given us a more scientific formula for calculating or measuring dispersion. while calculating SD we take deviations of individual observations from their arithmetic mean and then each squares. The sum of the squares is divided by total number of observations. The square root of this sum is known as standard deviation.  The standard deviation is the most useful and most popular measure of dispersion.  It is always calculated from the arithmetic mean, median and mode is not considered.  Standard deviation is the positive square root of the average of squared deviation taken from arithmetic mean. 2022 Standard deviation 5
6. 6. STANDARD DEVIATION FORMULA THE STANDARD DEVIATION IS REPRESENTED BY THE GREEK LETTER ‘ ‘ (SIGMA) FORMULA:- ALTERNATIVELY:- 𝜎 = 𝛴𝑥2 𝑁 − 𝑥 𝑁 2 2022 STANDARD DEVIATION 6 𝜎 = 𝑥 − 𝑥 2 𝑁
7. 7. METHODS OF CALCULATING STANDARD DEVIATION  CASE-1By taking deviations of the items from the actual mean.  CASE-2By taking deviations of the items from the assumed mean. 2022 Standard deviation 7
8. 8. MERITS OF STANDARD DEVIATION 2022 STANDARD DEVIATION 8
9. 9.  It is rigidly defined and based on all observations of the data.  It is least affected by sampling fluctuations.  It is possible to calculate combined standard deviation of two or more series.  Since the deviations are squared so they all become positive and difficulty of sign is not found here.  Standard deviation is used for further statistical treatments e.g skewness, correlation,sampling etc  Standard deviation enables us to determine the reliability of the means of two or more different series when these means are same.  With the help of standard deviation ,it is possible to ascertain the area under the normal curve.  It has great utility in hypothesis testing which other measures of dispersion hardly do. 2022 STANDARD DEVIATION 9
10. 10.  It is not simple to calculate and easy to understood.  It is also affected by extreme values. It gives undue importance to the items away from the arithmetic mean, and less importance to the items near the mean.  The chief limitations of standard deviation is that it cannot be used for comparing the dispersion of two or more series of observations given in different units.  Despite of these limitations, standard deviation fulfils all the requisites of a good measure of dispersion except that it is sensitive to extreme values. That is why it is known as standard deviation. 2022 Standard deviation 10
11. 11. SUMMARY  Standard deviation is an especially useful tool in investing and trading strategies as it helps measure market and security volatility and predict performance trends.  Standard deviation is one of the key fundamental risk measures that analysis portfolio managers, advisors use. 2022 Standard deviation 11
12. 12. THANK YOU SUBMITTED BY: SANSKRITI SEN MCOM (AFC) SEM 1 INVENTORY MANAGEMENT AND CONTROL