presentation on standard deviation

1. STANDARD
DEVIATION
SUBMITTED TO: NANCY

2. TABLE OF CONTENTS
° WHAT IS STANDARD DEVIATION?
° METHODS OF CALCULATING STANDARD DEVIATION
° OBJECTIVE OF STANDARD DEVIATION
° MERITS AND DEMERITS OF STANDARD DEVIATION
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° STANDARD DEVIATION FORMULA
° INTRODUCTION

3. SUMMARY MEASURES
SUMMARY
MEASURES
CENTRAL TENDENCY VARIATION
RANGE
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MEAN
MODE
MEDIAN
QUARTILE
DEVIATION STANDARD
DEVIATION
MEAN
DEVIATION

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
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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.
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6. STANDARD DEVIATION
FORMULA
THE STANDARD DEVIATION IS REPRESENTED BY THE
GREEK LETTER ‘ ‘ (SIGMA)
FORMULA:-
ALTERNATIVELY:-
𝜎 =
𝛴𝑥2
𝑁
−
𝑥
𝑁
2
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𝜎 =
𝑥 − 𝑥 2
𝑁

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.
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7

8. MERITS OF
STANDARD
DEVIATION
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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.
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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.
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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.
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12. THANK YOU
SUBMITTED BY: SANSKRITI SEN
MCOM (AFC)
SEM 1
INVENTORY MANAGEMENT AND CONTROL