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Variance and Standard Deviation, STANDARD DEVIATION OF UNGROUP DATA -…
Variance and Standard Deviation
UNGROUP DATA
Variance formula
Example Find the variance for an ungrouped 5,12,3,18,6,8,2,10
MEANING
In statistics, variance measures variability from the average or mean. It is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set.
FORMULA
Arranging the ungrouped data in ascending order
STANDARD DEVIATION
FORMULA STANDARD DEVIATION
MEANING
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently the squares of the differences are added.
GROUP DATA
VARIANCE FORMULA
MEANING
The variance formula measures how far a set of numbers are spread out. It is a numerical value and is used to indicate how widely individuals in a group vary. If individual observations vary considerably from the group mean, the variance is big and vice versa.
EXAMPLE
STANDARD DEVIATION
MEANING
Standard deviation calculates the dispersion of a dataset relative to its mean. If the data points are away from the mean, there is a higher deviation within the data set. Hence, the more spread out the data, the greater the standard deviation. Standard deviation cannot be negative.
FORMULA
σ² = Σ(Fi
Mi2) - (n
μ2) / (n - 1)
STANDARD DEVIATION EXAMPLE
STANDARD DEVIATION OF UNGROUP DATA
