Find the sample variance s2 for the following sample data. Round your answer to the nearest hundredth.
x: 23 17 12 35 29
a. 84.20
b. 67.36
c. 101.00
d. 88.84
e. 126.25
My TI 30x calculated it rather quickly. I am not certain of your question.
Calculate the mean, then the difference between the mean and each data point, square it, then sum the squares, then divide by n.
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To find the sample variance (s^2), we need to follow these steps:
1. Find the mean (average) of the sample data.
2. Subtract the mean from each data point and square the result.
3. Sum up all the squared differences.
4. Divide the sum by the number of data points minus 1.
Let's calculate the sample variance step by step for the given sample data:
1. Find the mean:
(23 + 17 + 12 + 35 + 29) / 5 = 116 / 5 = 23.2
2. Subtract the mean and square each difference:
(23 - 23.2)^2 ≈ 0.04
(17 - 23.2)^2 ≈ 38.44
(12 - 23.2)^2 ≈ 125.44
(35 - 23.2)^2 ≈ 138.24
(29 - 23.2)^2 ≈ 33.64
3. Sum up the squared differences:
0.04 + 38.44 + 125.44 + 138.24 + 33.64 ≈ 335.80
4. Divide the sum by the number of data points minus 1:
335.80 / (5 - 1) ≈ 335.80 / 4 ≈ 83.95
Rounding the sample variance to the nearest hundredth, we get 83.95.
Out of the given options, the closest value to 83.95 is option a. 84.20.