Bowen Garrett
10/05/2023 · High School

A particular brand of laptop was sampled with regard to the time it can be used before it requires recharging. The mean time was calculated to be 7.1 hours with a standard deviation of 1.94 hours. Calculate the coefficient of variation for this example. \( \mathrm{CV}=\square \% \) (Round to two decimal places as needed.)

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The coefficient of variation (CV) is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean, multiplied by 100 to express it as a percentage. The formula for the coefficient of variation is: \[ \text{CV} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 \] Given: Mean time = 7.1 hours Standard deviation = 1.94 hours Substitute the values into the formula to calculate the coefficient of variation. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{1.94}{7.1}\right)\times 100\) - step1: Divide the terms: \(\frac{97}{355}\times 100\) - step2: Reduce the numbers: \(\frac{97}{71}\times 20\) - step3: Multiply: \(\frac{97\times 20}{71}\) - step4: Multiply: \(\frac{1940}{71}\) The coefficient of variation for this example is approximately 27.32%.

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The coefficient of variation is approximately 27.32%.
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