Final answer:
The sample variance for the data (-6, 7, 7, 7, 15) is calculated to be 57, and the sample standard deviation, rounded to two decimal places, is 7.55.
Step-by-step explanation:
To compute the sample variance and standard deviation of the data sample (-6, 7, 7, 7, 15), we follow these steps:
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- Calculate the mean of the sample.
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- Subtract the mean from each data point and square the result.
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- Sum those squared differences.
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- Divide the sum by the sample size minus one to get the sample variance.
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- Take the square root of the variance to get the sample standard deviation.
Let's do the calculations:
1. Mean (μ) = (-6+7+7+7+15) / 5 = 30 / 5 = 6
2. The squared differences are: (-6-6)², (7-6)², (7-6)², (7-6)², (15-6)² = 144, 1, 1, 1, 81.
3. Sum = 144 + 1 + 1 + 1 + 81 = 228
4. Sample variance (s²) = 228 / (5-1) = 228 / 4 = 57
5. Sample standard deviation (s) = √57 = 7.55 (rounded to two decimal places)
Therefore, the sample variance is 57, and the standard deviation is 7.55.