Questions: Find (a) the range and (b) the standard deviation for the sample. Value Frequency 2 2 3 5 4 4 5 2 6 1 (a) The range is 4. (Round to one decimal place as needed.) (b) The standard deviation is 1.150. (Round to one decimal place as needed.)

Find (a) the range and (b) the standard deviation for the sample. Value Frequency 2 2 3 5 4 4 5 2 6 1 (a) The range is 4. (Round to one decimal place as needed.) (b) The standard deviation is 1.150. (Round to one decimal place as needed.)
Transcript text: Find (a) the range and (b) the standard deviation for the sample. \begin{tabular}{c|c} Value & Frequency \\ \hline 2 & 2 \\ 3 & 5 \\ 4 & 4 \\ 5 & 2 \\ 6 & 1 \end{tabular} (a) The range is 4 . (Round to one decimal place as needed.) (b) The standard deviation is 1.150 . (Round to one decimal place as needed.)
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Solution

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Solution Steps

Step 1: Finding the Range

The range is calculated as the difference between the maximum and minimum values. In this case, Range = 6 - 2 = 4.

Step 2: Finding the Standard Deviation

The standard deviation is calculated as the square root of the variance. Here, the variance is calculated based on the formula applicable to the data representation (frequency distribution or raw data). Finally, Standard Deviation = \(\sqrt{1.2} = 1.1\).

Final Answer:

The range of the data is 4 and the standard deviation is 1.1.

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