Questions: The average weekly unemployment benefits (in dollars) for a random selection of states are listed below. 272 239 289 214 276 252 190 209 251 272 310 321 Find the standard deviation. Round your answer to at least one decimal place. The standard deviation is 40.2 . Find the range rule of thumb. Round your answer to one decimal place.

The average weekly unemployment benefits (in dollars) for a random selection of states are listed below. 272 239 289 214 276 252 190 209 251 272 310 321 Find the standard deviation. Round your answer to at least one decimal place. The standard deviation is 40.2 . Find the range rule of thumb. Round your answer to one decimal place.
Transcript text: The average weekly unemployment benefits (in dollars) for a random selection of states are listed below. 272 239 289 214 276 252 190 209 251 272 310 321 Find the standard deviation. Round your answer to at least one decimal place. The standard deviation is 40.2 . Find the range rule of thumb. Round your answer to one decimal place.
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Solution

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Solution Steps

To find the range rule of thumb, we need to calculate the range of the data set and then use the range rule of thumb formula, which states that the standard deviation is approximately the range divided by 4.

Solution Approach
  1. Calculate the range of the data set by subtracting the minimum value from the maximum value.
  2. Apply the range rule of thumb formula: standard deviation ≈ range / 4.
  3. Round the result to one decimal place.
Step 1: Calculate the Range

The range of the data set is calculated by subtracting the minimum value from the maximum value: \[ \text{Range} = \max(\text{data}) - \min(\text{data}) = 321 - 190 = 131 \]

Step 2: Apply the Range Rule of Thumb

The range rule of thumb states that the standard deviation is approximately the range divided by 4: \[ \text{Standard Deviation} \approx \frac{\text{Range}}{4} = \frac{131}{4} = 32.75 \]

Step 3: Round the Result

Round the result to one decimal place: \[ \text{Standard Deviation} \approx 32.8 \]

Final Answer

The range rule of thumb is \(\boxed{32.8}\).

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