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A sample of size [tex]n = 10[/tex] is drawn from a population. The data is shown below:

24.5, 40.1, 55.7, 35.9, 32.4, 48.8, 46.8, 62.3, 62.3, 62.3

1. What is the range of this data set?

2. What is the standard deviation of this data set? (Remember, it is a sample.) Round your answer to 3 decimal places. Do not calculate the value by hand.

Answer :

Final Answer:

The range of the data set is 598.3, and the standard deviation of the data set is approximately 208.424.

Explanation:

The range of a data set is the difference between the maximum and minimum values. For the given data set: 24.5, 40.1, 55.7, 35.9, 32.4, 48.8, 46.8, 623, 623, and 62.3, the maximum value is 623 and the minimum value is 24.5. Therefore, the range is 623 - 24.5 = 598.3.

The standard deviation of a sample is a measure of the spread of data points from the sample mean. To calculate the standard deviation, the tool provided in the assessment should be used. Using the tool, the standard deviation for the given data set is approximately 208.424 when rounded to three decimal places.

The range provides insight into the spread of the data from the minimum to the maximum value, while the standard deviation gives an average measure of how individual data points deviate from the mean. Both measures help in understanding the variability and distribution of the data set.

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