The document introduces the concepts of variance and standard deviation. Variance is a statistical measure that quantifies how far observations in a data set spread out from the mean or average value. It is calculated by taking the average of the squared differences from the mean. Standard deviation is the square root of variance and represents how dispersed the values in a data set are from the mean. The document provides examples of computing variance and standard deviation to illustrate these statistical concepts.

1. Understanding Variance and
Standard Deviation
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2. You will be introduced thro’
• The concept of variance
• Computation of Variance
• Computation of Standard Deviation
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3. Variance
• Variance is often used as a measure of
risk in finance. It is a statistical concept
whose purpose is to measure the
dispersion of observation around the mean
or the average value.
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4. The concept of variance
• Lets consider that in a poll, we took 10
students and their ages are as per below
• 21, 20, 19, 23, 22, 21, 20, 18, 19, 19
• Lets put them in order...
Range tells us about
the dispersion of
values in sample
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5. The concept of variance
• Range only depends on the highest and the
lowest value in the sample, and not how
observations are distributed.
• This bring us to variance.
• Variance is a measure, very much like arithmetic
mean which takes every observation into
account. It gives equal weight to all observations
and measures the dispersion around the central
tendency.
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6. Example
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7. Let’s put’em to Histogram
• Histogram is a visual representation of the
variable of interest (Student’s age) and
their frequency.
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8. Lets join the bars...
If we expand our selection to more observations or
full population, above graph can be more smooth and
can have bell shape…..
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9. Lets get back to the concept of Variance
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10. Variance
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11. How to Compute Variance?
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12. How to Compute Variance?
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13. How to Compute Variance?
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14. How to Compute Variance?
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15. Computation of Variance for a set of
historical observation.
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16. Solution
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17. Computation of Variance for
probability distribution
• Below is the table of attendance in football
stadium
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19. Computation of Standard Deviation
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