Find the variance for the given data. Round your answer to two decimal places.
5.0, 8.0, 4.9, 6.8, and 2.8
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
To find the variance for a set of data, follow these steps:
Step 1: Find the mean (or average) of the data set.
To find the mean, add up all the numbers in the data set and then divide the sum by the total number of data points.
For the given data set, the sum is: 5.0 + 8.0 + 4.9 + 6.8 + 2.8 = 27.5
And there are 5 data points. So the mean is: 27.5 / 5 = 5.5
Step 2: Subtract the mean from each data point.
Subtract the mean (5.5) from each data point. This gives us a measure of how much each data point deviates from the mean.
The deviations from the mean for each data point are:
5.0 - 5.5 = -0.5
8 - 5.5 = 2.5
4.9 - 5.5 = -0.6
6.8 - 5.5 = 1.3
2.8 - 5.5 = -2.7
Step 3: Square each deviation.
Square each deviation calculated in step 2. Squaring eliminates the negative signs and makes all values positive.
(-0.5)^2 = 0.25
2.5^2 = 6.25
(-0.6)^2 = 0.36
1.3^2 = 1.69
(-2.7)^2 = 7.29
Step 4: Find the average of the squared deviations.
Add up all the squared deviations calculated in step 3 and divide by the total number of data points.
(0.25 + 6.25 + 0.36 + 1.69 + 7.29) / 5 = 3.37
Step 5: Round the variance to two decimal places.
The variance is the average of the squared deviations. Rounding to two decimal places gives us the final answer.
Variance = 3.37 (rounded to two decimal places)
To find the variance for the given data, follow these steps:
Step 1: Find the mean of the data set.
To find the mean, sum up all the numbers in the data set and divide the result by the total number of values.
Mean = (5.0 + 8.0 + 4.9 + 6.8 + 2.8) / 5
Mean = 27.5 / 5
Mean = 5.5
Step 2: Subtract the mean from each value in the data set.
Subtract the mean (5.5) from each value and square the result.
(5.0 - 5.5)^2 = 0.25
(8.0 - 5.5)^2 = 6.25
(4.9 - 5.5)^2 = 0.36
(6.8 - 5.5)^2 = 1.69
(2.8 - 5.5)^2 = 7.84
Step 3: Find the sum of the squared differences.
Sum up all the squared differences obtained from Step 2.
0.25 + 6.25 + 0.36 + 1.69 + 7.84 = 16.39
Step 4: Divide the sum of squared differences by the total number of values.
Variance = Sum of squared differences / Total number of values
Variance = 16.39 / 5
Variance ≈ 3.28 (rounded to two decimal places)
Therefore, the variance for the given data set is approximately 3.28.