Answer to Question #115310 in Statistics and Probability for Michael

Question

Choose a measure of central tendency and discuss why it would or not be effective “statistical summary” for a given data set .

Answer 1

The measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. We have 3 measures of central tendency: mean, median and mode.

It’s best to use the mean as a measure of the central tendency when you have a symmetric distribution. Because if a distribution is skewed mean falls outside the central area. Outliers have a substantial impact on the mean.

Ouliers and skewed data have a smaller effect on the median. When you have a skewed distribution, the median is a better measure of central tendency than the mean. For example we will consider two datasets:

1) 69, 56, 54, 52, 47, 46, 46, 45, 43, 36, 35, 34, 31.

2) 112, 93, 89, 82, 47, 46, 46, 45, 43, 36, 35, 34, 31.

For the first dataset median equals 46. For the second dataset median is also 46. But the only difference of these two datasets is that the first four values are different. The second distribution is skewed with large outliers.

We use a mode with categorical, ordinal and discrete data. If no value repeats, the data do not have a mode. With continuous data, it is unlikely that two or more values will be exactly equal. So we do not use a mode for continuous data.