Find variance given if am =?
Introduction:
Variance is a statistical measure that calculates the spread or variability of a set of data points around their mean. It is a measure of how far each value in the data set is from the mean.
Formula:
The formula for variance is as follows:
Variance = (Σ (xi – μ)²) / n
Where:
Σ = Summation
xi = ith value in the data set
μ = Mean of the data set
n = Total number of values in the data set
Steps to find variance:
1. Calculate the mean of the data set.
2. Subtract the mean from each value in the data set to find the deviation from the mean.
3. Square the deviations.
4. Add the squared deviations.
5. Divide the sum of squared deviations by the total number of values in the data set.
Example:
Suppose we have the following data set:
3, 5, 7, 9, 11
To find the variance of this data set, we follow these steps:
1. Calculate the mean of the data set.
Mean = (3+5+7+9+11) / 5 = 7
2. Subtract the mean from each value to find the deviation from the mean.
Deviations: -4, -2, 0, 2, 4
3. Square the deviations.
Squared deviations: 16, 4, 0, 4, 16
4. Add the squared deviations.
Sum of squared deviations: 40
5. Divide the sum of squared deviations by the total number of values in the data set.
Variance = 40 / 5 = 8
Therefore, the variance of the data set is 8.
Conclusion:
In conclusion, variance is an important statistical measure that helps to quantify the spread or variability of a set of data points around their mean. It is calculated by finding the sum of squared deviations from the mean and dividing by the total number of values in the data set.