what is the variance of 18, 16, 12, 2, 11
Variance =38.2
To find the variance of a set of data, follow these steps:
Step 1: Calculate the mean (average) of the data set.
Step 2: Subtract the mean from each number in the data set.
Step 3: Square each of the differences obtained in step 2.
Step 4: Calculate the mean of the squared differences obtained in step 3.
Let's calculate the variance of the given data set: 18, 16, 12, 2, 11.
Step 1: Calculate the mean.
Mean = (18 + 16 + 12 + 2 + 11) / 5
Mean = 59 / 5
Mean = 11.8
Step 2: Subtract the mean from each number.
18 - 11.8 = 6.2
16 - 11.8 = 4.2
12 - 11.8 = 0.2
2 - 11.8 = -9.8
11 - 11.8 = -0.8
Step 3: Square each difference.
6.2^2 = 38.44
4.2^2 = 17.64
0.2^2 = 0.04
(-9.8)^2 = 96.04
(-0.8)^2 = 0.64
Step 4: Calculate the mean of the squared differences.
Mean of squared differences = (38.44 + 17.64 + 0.04 + 96.04 + 0.64) / 5
Mean of squared differences = 152.8 / 5
Mean of squared differences = 30.56
Therefore, the variance of the given data set is 30.56.
To find the variance of a set of numbers, you need to follow these steps:
1. Find the mean (average) of the numbers. To do this, add up all the numbers and divide the sum by the total number of numbers.
In this case, the sum of the numbers is 18 + 16 + 12 + 2 + 11 = 59.
There are 5 numbers in total, so the mean is 59/5 = 11.8.
2. Subtract the mean from each number in the set, and square the result.
For example, subtracting the mean from 18 gives: (18 - 11.8)^2 = 42.25.
Do this for each number in the set.
3. Find the mean of the squared differences. Add up all the squared differences and divide the sum by the total number of numbers.
For this set, the squared differences are: 42.25, 18.49, 0.64, 78.44, and 0.64.
The sum of these squared differences is 140.46.
Since there are 5 numbers, the mean of the squared differences is 140.46/5 = 28.09.
Therefore, the variance of the numbers 18, 16, 12, 2, and 11 is 28.09.