Find the sample variance s2 for the following sample data. Round your answer to the nearest hundredth.
x:
23
17
12
35
29
To find the sample variance, follow these steps:
Step 1: Find the sample mean (x̄).
x̄ = (23 + 17 + 12 + 35 + 29) / 5
= 116 / 5
= 23.2
Step 2: Find the deviation of each value from the mean and square it.
Deviation of 23 from the mean = (23 - 23.2)² = 0.04
Deviation of 17 from the mean = (17 - 23.2)² = 38.44
Deviation of 12 from the mean = (12 - 23.2)² = 124.84
Deviation of 35 from the mean = (35 - 23.2)² = 138.24
Deviation of 29 from the mean = (29 - 23.2)² = 33.64
Step 3: Find the sum of all squared deviations.
Sum of squared deviations = 0.04 + 38.44 + 124.84 + 138.24 + 33.64
= 335.2
Step 4: Divide the sum of squared deviations by (n - 1), where n is the sample size.
s² = Sum of squared deviations / (n - 1)
= 335.2 / (5 - 1)
= 335.2 / 4
= 83.8
Therefore, the sample variance (s²) is 83.8.
To find the sample variance, you will need to follow these steps:
1. Calculate the sample mean (x̄) of the given data set.
To find the sample mean, add up all the values in the data set and then divide the sum by the total number of data points:
(23 + 17 + 12 + 35 + 29) / 5 = 116 / 5 = 23.2
So, the sample mean (x̄) is 23.2.
2. Calculate the deviation of each data point from the sample mean.
For each data point, subtract the sample mean (23.2) from the data point. Here are the deviations for each data point:
23 - 23.2 = -0.2
17 - 23.2 = -6.2
12 - 23.2 = -11.2
35 - 23.2 = 11.8
29 - 23.2 = 5.8
3. Square each deviation obtained in step 2.
For each deviation, square the value:
(-0.2)^2 = 0.04
(-6.2)^2 = 38.44
(-11.2)^2 = 125.44
(11.8)^2 = 139.24
(5.8)^2 = 33.64
4. Sum up the squared deviations obtained in step 3.
Add up all the squared deviations:
0.04 + 38.44 + 125.44 + 139.24 + 33.64 = 336.8
5. Divide the sum obtained in step 4 by (n-1), where n is the total number of data points.
In this case, n = 5, so:
336.8 / (5-1) = 336.8 / 4 = 84.2
6. Round the result to the nearest hundredth.
The sample variance (s^2) is approximately 84.2 when rounded to the nearest hundredth.
Therefore, the sample variance (s^2) for the given sample data is approximately 84.2.
Find the mean first, then subtract the mean from each score and square each difference. Sum those differences and divide by n to get the variance.
By the way, "^" is used online to indicate an exponent, e.g., x^2 = x squared.