This document defines variance and standard deviation, which are measures of how spread out numbers are in a data set from the mean. It explains how to calculate variance by finding the mean, subtracting it from each value, squaring the deviations, summing them and dividing by the number of items. Standard deviation is the square root of variance and measures how far data points on average lie from the mean, with a higher value indicating more dispersion from the mean. Formulas for calculating both are provided.

1. STANDARD DEVIATION
AND VARIATION
ERRORS IN MEASUREMENT:

2. Objectives
• To find the variance of a data set.
• To find the standard deviation of a data set.

3. Variance
◦ Variance is the average squared deviation from the
mean of a set of data.
◦ It is used to find the standard deviation.

4. Variance
-- Find the mean of the data.
-Mean is the average so add up the values and divide by the number
of items.
-- Subtract the mean from each value – the result is called the deviation
from the mean.
-- Square each deviation of the mean.
-- Find the sum of the squares.
-- Divide the total by the number of items.

5. Variance Formula
The variance formula includes the Sigma Notation, , which
represents the sum of all the items to the right of Sigma.

2
( )x
n

Mean is represented by and n is the number of items.

6. Standard Deviation
• is a special form of average deviation from the
mean.
• is the positive square root of the arithmetic mean of
the squared deviations from the mean of the
distribution.

7. Standard Deviation:
• is considered as the most reliable measure of
variability.
• is affected by the individual values or items in the
distribution.

8. Standard Deviation Formula
The standard deviation formula can be represented
using Sigma Notation:
2
( )x
n



 
The standard deviation formula is the square root of
the variance.

9. GRAPH:

10. Conclusion
•As we have seen, standard deviation measures the
dispersion of data.
•The greater the value of the standard deviation, the further
the data tend to be dispersed from the mean.

11. Thank You!!