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Answer:
To calculate the standard deviation, follow these steps:
1. Calculate the mean (average) of the data set. In this case, the mean is approximately 30.1333.
2. Find the difference between each data point and the mean. Square these differences.
3. Find the average of these squared differences. This is the variance.
4. Take the square root of the variance to find the standard deviation.
Here's the calculation for your data set:
1. Mean (μ) = Σxi / n = 452 / 15 ≈ 30.1333
2. Subtract the mean from each data point and square the result:
(15-30.1333)^2 ≈ 232.0156
(20-30.1333)^2 ≈ 103.9325
(22-30.1333)^2 ≈ 67.9469
(22-30.1333)^2 ≈ 67.9469
(22-30.1333)^2 ≈ 67.9469
(25-30.1333)^2 ≈ 26.7333
(25-30.1333)^2 ≈ 26.7333
(27-30.1333)^2 ≈ 10.9978
(28-30.1333)^2 ≈ 4.5406
(33-30.1333)^2 ≈ 8.5329
(34-30.1333)^2 ≈ 13.7733
(39-30.1333)^2 ≈ 76.0689
(43-30.1333)^2 ≈ 166.8769
(48-30.1333)^2 ≈ 317.2178
(49-30.1333)^2 ≈ 358.4289
3. Sum these squared differences:
Σ(x-μ)^2 ≈ 1150.4424
4. Calculate the variance:
Variance (σ^2) = Σ(x-μ)^2 / n = 1150.4424 / 15 ≈ 76.6962
5. Finally, calculate the standard deviation:
Standard Deviation (σ) = √(Variance) = √76.6962 ≈ 8.7551
So, the standard deviation of the given data set is approximately 8.7551.