Question

Which of the following correctly describes a limitation or strength of using a measure of central tendency?

a) the mode is susceptible to outliers, as very small or very large numbers can change where the middle falls.
b) the mode is most effective when using non-numerical data sets, as the data point that occurs most often can be calculated with categorical data.
c) the median is susceptible to outliers, as very small or very large numbers change where the middle falls.
d) the mean is most effective when using non-numerical data sets, as the average will indicate the most common selection.

Answer 1

Option b is correct because the mode is effective for non-numerical data sets in identifying the most frequently occurring category. The median is less influenced by outliers than the mean, making it more reliable for skewed data sets. The mean is sensitive to outliers and best used for symmetrical distributions.

Step-by-step explanation:

The description that correctly identifies a limitation or strength of using a measure of central tendency is option b) the mode is most effective when using non-numerical data sets, as the data point that occurs most often can be calculated with categorical data. The mode is useful in this context because it identifies the most frequently occurring category, which is meaningful in qualitative data analysis.

Conversely, the median and mean are more appropriate for numerical data. The median is useful for skewed distributions or when a data set contains outliers, as it does not get affected by the extreme values. Meanwhile, the mean provides a good estimate of the central tendency for symmetrically distributed data, but it is sensitive to outliers, which can significantly influence the calculated average.