A college professor collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday’s Business Statistics exam. He processed the data by Excel and the following incomplete output is available. Mean 7Sample Variance 7.84Skewness 1.17 The coefficient of variation in the data is __________.Multiple Choice40%243%111%90%
Question
A college professor collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday’s Business Statistics exam. He processed the data by Excel and the following incomplete output is available. Mean 7Sample Variance 7.84Skewness 1.17 The coefficient of variation in the data is __________.Multiple Choice40%243%111%90%
Solution
The coefficient of variation is a measure of relative variability. It is the ratio of the standard deviation to the mean, and it is often expressed as a percentage.
Here are the steps to calculate it:
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First, we need to find the standard deviation. The standard deviation is the square root of the variance. Given that the variance is 7.84, the standard deviation is sqrt(7.84) = 2.8.
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Next, we calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100 to get a percentage. The mean is given as 7.
So, the coefficient of variation = (2.8 / 7) * 100 = 40%.
Therefore, the coefficient of variation in the data is 40%.
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