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Answer :
Final answer:
To find the standard deviation for the given sample data, use the formula: Standard deviation = sqrt((sum of (x - mean)^2) / (n - 1)). Calculate the mean, find the sum of (x - mean)^2, divide by (n - 1), and take the square root to get the standard deviation. The standard deviation for the given sample data is approximately 8.16.
Explanation:
To find the standard deviation for the given sample data, we can use the formula:
Standard deviation = sqrt((sum of (x - mean)^2) / (n - 1))
where x is the value of each data point, mean is the average of the data, and n is the number of data points.
Calculating the standard deviation for the given sample data:
Find the mean of the data by adding up all the values and dividing by the number of values. In this case, the mean is (14.7 + 15.1 + 31.6 + 42.6 + 17.7 + 18.8) / 6 = 23.5- Calculate the sum of (x - mean)^2 for each data point, where x is the value of each data point and mean is the calculated mean. For example, (14.7 - 23.5)^2 = 82.81
- Add up all the results from step 2 to get the sum of (x - mean)^2, which is 266.09
- Divide the sum of (x - mean)^2 by (n - 1), where n is the number of data points. In this case, (266.09 / (6-1)) = 66.5225
- Take the square root of the result from step 4 to find the standard deviation. The square root of 66.5225 is approximately 8.16
Therefore, the standard deviation for the given sample data is approximately 8.16.
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