A sample consists of the following data 7,11,12,18,20,22,25. What is the sample variance?
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.
I'll let you do the calculations.
I got 42.95
To find the sample variance, follow these steps:
1. Calculate the mean (average) of the sample data:
Mean = (7 + 11 + 12 + 18 + 20 + 22 + 25) / 7 = 115 / 7 = 16.4286 (rounded to 4 decimal places)
2. Subtract the mean from each data point and square the result for each data point:
(7 - 16.4286)^2 ≈ 79.2857
(11 - 16.4286)^2 ≈ 29.0612
(12 - 16.4286)^2 ≈ 19.2820
(18 - 16.4286)^2 ≈ 2.6747
(20 - 16.4286)^2 ≈ 12.2449
(22 - 16.4286)^2 ≈ 31.4898
(25 - 16.4286)^2 ≈ 74.5306
3. Add up all the squared differences:
79.2857 + 29.0612 + 19.2820 + 2.6747 + 12.2449 + 31.4898 + 74.5306 ≈ 249.5699
4. Divide the sum by (n - 1), where n is the number of data points in the sample (in this case, n = 7):
Variance = 249.5699 / (7 - 1) ≈ 41.5949
Therefore, the sample variance is approximately 41.5949.
To find the sample variance, you can follow these steps:
1. Find the mean (average) of the sample data.
Add up all the values in the sample: 7 + 11 + 12 + 18 + 20 + 22 + 25 = 115.
Divide the sum by the number of observations: 115 / 7 = 16.43 (rounded to two decimal places).
2. Calculate the deviation from the mean for each individual value.
Subtract the mean from each data point:
7 - 16.43 = -9.43
11 - 16.43 = -5.43
12 - 16.43 = -4.43
18 - 16.43 = 1.57
20 - 16.43 = 3.57
22 - 16.43 = 5.57
25 - 16.43 = 8.57
3. Square each deviation.
Square each of the previously calculated deviations:
(-9.43)^2 = 88.84
(-5.43)^2 = 29.52
(-4.43)^2 = 19.60
(1.57)^2 = 2.46
(3.57)^2 = 12.73
(5.57)^2 = 31.02
(8.57)^2 = 73.47
4. Find the sum of the squared deviations.
Add up all the squared deviations:
88.84 + 29.52 + 19.60 + 2.46 + 12.73 + 31.02 + 73.47 = 257.64
5. Divide the sum of the squared deviations by (n-1), where n is the sample size.
In this case, n = 7, so divide 257.64 by 6: 257.64 / 6 = 42.94 (rounded to two decimal places).
Therefore, the sample variance is 42.94.