Sure, let's calculate the variance for the given dataset, which consists of the numbers 12, 20, 25, 5 and 7.
The variance is a measure of how spread out the numbers in a data set are. It’s mathematically defined as the average of the squared differences from the mean.
To calculate the variance, we will follow these stages:
1. Calculate the Mean value (the average)
First, we add up all the numbers in the dataset and then divide by the count of numbers,
Mean = (12 + 20 + 25 + 5 + 7) / 5 = 13.8
2. Subtract the Mean and square the result (the squared difference)
Next, we need to subtract the Mean from each number in the data set and then square the result.
(12-13.8)² = 3.24
(20-13.8)² = 38.44
(25-13.8)² = 125.44
(5-13.8)² = 77.44
(7-13.8)² = 46.24
3. Calculate the average of those squared differences.
Finally, we will take average of the calculated squared numbers.
(3.24 + 38.44 + 125.44 + 77.44 + 46.24) / 5 = 58.16
So, the Variance of the given dataset {12, 20, 25, 5, 7} is 58.16 when rounded to 2 decimal places.
For the purpose of calculation here, we have used the method of Variance calculation for a population, not a sample. The method slightly differs if you wish to calculate the variance of a sample. The method used here assumes that you are working with an entire population.