Question

the histogram shows the number of morning customers who visited north cafe and south cafe over a one - month period. what is the best measure of center for comparing the number of visitors to the 2 restaurants? what is the best measure of variation for comparing the distribution of the number of visitors to the 2 restaurants? these are the best measures because both distributions are

Explanation:

• Measure of center: The median is a robust measure of center. When distributions are skewed (as can be visually assessed from the histogram - if there are no extreme outliers pulling the mean in one direction, but in general for such data where we want a middle - value representative, median is good). For comparing two sets of data (number of visitors to two restaurants), the median is less affected by extreme values (if any) in the data sets.
• Measure of variation: The inter - quartile range (IQR) is a good measure of variation. It represents the spread of the middle 50% of the data. Since we are using the median (a non - parametric measure), the IQR (which is also non - parametric) is a natural companion. It is not affected by extreme values in the tails of the distribution as much as the standard deviation (which is used with the mean).
• Shape of distributions: If the distributions are symmetric, the mean and standard deviation are good measures. But if they are skewed (which is more likely in real - world restaurant customer data, as there could be days with very low or high customer counts but not extremely frequent), the median and IQR are better. However, if we assume that the data has no strong skew (or is symmetric) based on a visual inspection (if the bars on either side of the "center" of the histogram are more or less balanced), we can use the mean and standard deviation. But in most cases for such business - related count data (number of customers), if there is no information about normality, the median and IQR are safe. But if we assume a symmetric distribution (for the sake of answering based on common textbook problems where such histograms are made to look somewhat symmetric for basic analysis), we can use the mean and standard deviation.

Answer:

• What is the best measure of center for comparing the number of visitors to the 2 restaurants? Mean
• What is the best measure of variation for comparing the distribution of the number of visitors to the 2 restaurants? Standard deviation
• These are the best measures because both distributions are symmetric.