Question

The dot plot shows the number of sandwiches made in a day by 11 chefs of a restaurant. Is the median or the mean a better center for this data and why?

a) Mean; because the data is skewed and clusters on the right
b) Mean; because the data is normally distributed with two outliers
c) Median; because the data is skewed and clusters on the right
d) Median; because the data is normally distributed with two outliers

Answer 1

The median is a better measure of center for the dataset because the data is skewed to the right, and the median is less affected by skew and outliers than the mean.

Step-by-step explanation:

When determining whether the median or the mean is a better measure of center for a dataset, it is essential to consider the distribution of the data. If the data is skewed, the mean is influenced more by extreme values or outliers than the median. Since the dot plot shows that the data is skewed and clusters to the right, it indicates a right-skewed distribution. In such cases, the median tends to be a more reliable measure of center because it is less affected by the skew and outliers. Therefore, the correct answer to which measure is better as a center for this data is: c) Median; because the data is skewed and clusters on the right. This is supported by information stating that when data are skewed, the median is less influenced by extreme values and reflects the central tendency of the dataset more accurately than the mean, which can be pulled by the skewness.