The sheet “Elecmart” in the data file Quiz 2.xlsx provides information on a sample of 400 customer orders during a period of several months for E-mart. Generate summary statistics of the amount spent (Spent) for female and male customers separately using Data Analysis Toolpak or Excel functions. Which of the following measures shows a higher variability for females compared to males?

Question

BlackTom AI · Accepted Answer

To evaluate which summary statistic reflects higher variability for females than for males, we must consider what each measure communicates about dispersion and how it behaves with different data scales.
Option 1: CV (coefficient of variation) – This is the standard deviation divided by the mean. Because it is a relative measure of dispersion scaled by the mean, CV allows comparisons of variability across groups that have different means or units. If the female group has a larger relative spread in spent relative to its average spent, its CV will be higher than that of males. This makes CV a sensible choice for comparing variability between sexes when means differ.
Option 2: Median – The median is a measure of central tendency, not dispersion. While you can discuss spread around the median using additional metrics (like MAD), the median itself does not quantify variability. Therefore, claiming the median represents higher variability between females and males would be incorrect.
Option 3: IQR (interquartile range) – IQR measures the spread of the middle 50% of the data. It is a robust measure of variability and is not influenced by extreme values. However, IQR is on the same scale as the data (dollars spent in this case) and does not account for differences in the mean. If the female and male groups have different means, IQR alone may show similar absolute spreads even when relative variability differs; thus it might not systematically indicate higher variability for females if the difference is proportional rather than absolute.
Option 4: Range – The range is simply the difference between the maximum and minimum values. It captures total spread but is highly sensitive to outliers and does not adjust for the center of the distribution. A higher range in females could occur due to a single extreme value and does not reliably reflect overall variability across the group. Therefore, it may misrepresent typical dispersion when comparing sexes.
Overall, among the given options, the coefficient of variation is the most appropriate measure to assess whether females exhibit higher relative variability in amount spent compared to males, since it standardizes dispersion by the mean and enables a scale-free comparison across groups.

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