Question

Which of the following values is closest to the standard deviation for the given data set: 99, 78, 56, 11, 43, 22, 16, 31, 49, 28, 37, 29, 30, 38, 34?

A) 23.2
B) 27.5
C) 25.9
D) 29.3

Answer 1

The standard deviation is calculated by finding the mean, subtracting it from each data value, squaring, summing, dividing by one less than the number of data points, and taking the square root. The closest value to the standard deviation of the given data set is 25.9.

Step-by-step explanation:

The question asks to find the standard deviation of a given data set. The formula for the sample standard deviation (s) is: s = \( \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \overline{x})^2} \), where \(x_i\) are the data points, \(\overline{x}\) is the mean of the data set, and n is the number of data points. To answer this question, follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Sum all the squared differences.
4. Divide the sum by one less than the number of data points (n-1).
5. Take the square root of the result from step 4 to get the standard deviation.

Using a calculator or software to compute this for the given data set, we would find that the standard deviation is closest to option C) 25.9.