We appreciate your visit to For the following set of data find the sample standard deviation to the nearest thousandth 86 83 76 82 67 69 82 82 69. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the sample standard deviation for the given data set, follow these steps:
1. List the Data: Start with the data set provided: 86, 83, 76, 82, 67, 69, 82, 82, 69.
2. Calculate the Mean:
- First, sum all the numbers: 86 + 83 + 76 + 82 + 67 + 69 + 82 + 82 + 69 = 696.
- Next, divide the sum by the number of values to find the mean: 696 / 9 = 77.33 (to two decimal places).
3. Find Each Deviation from the Mean:
- Subtract the mean from each data value to find the deviations:
- 86 - 77.33 = 8.67
- 83 - 77.33 = 5.67
- 76 - 77.33 = -1.33
- 82 - 77.33 = 4.67
- 67 - 77.33 = -10.33
- 69 - 77.33 = -8.33
- 82 - 77.33 = 4.67
- 82 - 77.33 = 4.67
- 69 - 77.33 = -8.33
4. Square Each Deviation:
- Convert each deviation to a squared value:
- 8.67² = 75.23
- 5.67² = 32.14
- (-1.33)² = 1.77
- 4.67² = 21.81
- (-10.33)² = 106.69
- (-8.33)² = 69.39
- 4.67² = 21.81
- 4.67² = 21.81
- (-8.33)² = 69.39
5. Calculate the Variance:
- Find the average of these squared differences, adjusting for sample variance:
- Sum of squared differences: 75.23 + 32.14 + 1.77 + 21.81 + 106.69 + 69.39 + 21.81 + 21.81 + 69.39 = 420.
- Divide by the number of data points minus one (N - 1): 420 / (9 - 1) = 52.5.
6. Calculate the Standard Deviation:
- The sample standard deviation is the square root of the variance:
- √52.5 = 7.246 (rounded to the nearest thousandth).
So, the sample standard deviation for the given data set is approximately 7.246.
1. List the Data: Start with the data set provided: 86, 83, 76, 82, 67, 69, 82, 82, 69.
2. Calculate the Mean:
- First, sum all the numbers: 86 + 83 + 76 + 82 + 67 + 69 + 82 + 82 + 69 = 696.
- Next, divide the sum by the number of values to find the mean: 696 / 9 = 77.33 (to two decimal places).
3. Find Each Deviation from the Mean:
- Subtract the mean from each data value to find the deviations:
- 86 - 77.33 = 8.67
- 83 - 77.33 = 5.67
- 76 - 77.33 = -1.33
- 82 - 77.33 = 4.67
- 67 - 77.33 = -10.33
- 69 - 77.33 = -8.33
- 82 - 77.33 = 4.67
- 82 - 77.33 = 4.67
- 69 - 77.33 = -8.33
4. Square Each Deviation:
- Convert each deviation to a squared value:
- 8.67² = 75.23
- 5.67² = 32.14
- (-1.33)² = 1.77
- 4.67² = 21.81
- (-10.33)² = 106.69
- (-8.33)² = 69.39
- 4.67² = 21.81
- 4.67² = 21.81
- (-8.33)² = 69.39
5. Calculate the Variance:
- Find the average of these squared differences, adjusting for sample variance:
- Sum of squared differences: 75.23 + 32.14 + 1.77 + 21.81 + 106.69 + 69.39 + 21.81 + 21.81 + 69.39 = 420.
- Divide by the number of data points minus one (N - 1): 420 / (9 - 1) = 52.5.
6. Calculate the Standard Deviation:
- The sample standard deviation is the square root of the variance:
- √52.5 = 7.246 (rounded to the nearest thousandth).
So, the sample standard deviation for the given data set is approximately 7.246.
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