Question

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data.

Data: 22.3, 23.2, 40.2, 41.3

a) 12.2
b) 14.9
c) 4,728.1
d) 40.8

Answer 1

The standard deviation for the sample data (22.3, 23.2, 40.2, 41.3) is 9.2 when following the proper calculation steps. However, this result does not match any of the provided answer choices, suggesting a potential error in the options or the need for clarification.

Step-by-step explanation:

To find the standard deviation for the sample data provided (22.3, 23.2, 40.2, 41.3), follow these steps:

1. Calculate the mean (average) of the data.
2. Subtract the mean from each data point and square the result.
3. Add up all the squared results.
4. Divide by the number of data points minus one (n-1) to get the sample variance.
5. Take the square root of the variance to get the sample standard deviation.

When you perform these calculations, you'll find that the sample standard deviation (rounded to one more decimal place than the original data as per the question guidelines) is 9.2.

None of the answer choices (a) 12.2, (b) 14.9, (c) 4,728.1, or (d) 40.8 match the calculated standard deviation. It's possible that there might be a mistake in the available options or in the calculation. If checking the calculation, and it's still correct, you would need to follow up for clarification on the answer choices provided.