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%.
Quick Answer
The coefficient of variation is approximately 27.32%.
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