To find the mean, variance, and standard deviation of ungrouped data, follow these steps:
1. Write down all the values of the data set.
2. Find the mean by summing up all the values and dividing by the number of values. The formula for mean is: Mean = sum of all values / number of values.
3. Subtract the mean from each value and square the result. These squared differences are called deviations.
4. Find the variance by summing up all the squared deviations and dividing by the number of values. The formula for variance is: Variance = sum of squared deviations / number of values.
5. Find the standard deviation by taking the square root of the variance. The formula for standard deviation is: Standard Deviation = Square root of variance.
Example:
Let's say we have the following ungrouped data set: 5, 7, 9, 11, 13.
1. There are 5 values in the data set.
2. The mean is (5 + 7 + 9 + 11 + 13) / 5 = 9.
3. The deviations from the mean are: -4, -2, 0, 2, 4.
4. The variance is (16 + 4 + 0 + 4 + 16) / 5 = 8.
5. The standard deviation is the square root of the variance, which is √8 ≈ 2.83.
So, the mean of the data set is 9, the variance is 8, and the standard deviation is 2.83.
How to find the mean, variance and standard deviation of the ungrouped data?
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