Which measure of central tendency is most affected by skewed data?

The measure of central tendency that is most affected by skewed data is the mean.

Step 1: Understanding the measures of central tendency The three main measures of central tendency are the mean, median, and mode. The mean is the average of all the numbers in a data set. The median is the middle number when the data set is ordered from least to greatest. The mode is the number that appears most frequently in a data set.

Step 2: Understanding skewed data Skewed data is data that is not symmetrically distributed. It can be positively skewed (where the tail on the right side is longer or fatter than the left side) or negatively skewed (where the tail on the left side is longer or fatter than the right side).

Step 3: Impact of skewed data on measures of central tendency The mean is calculated by adding all the numbers in the data set and dividing by the number of values. Therefore, if there are extremely high or low values (which is often the case in skewed data), the mean will be affected more than the median or mode. The median and mode are less sensitive to extreme values, and therefore are less affected by skewed data.

So, the mean is the measure of central tendency most affected by skewed data.

The measure of central tendency that is most affected by skewed data is the mean.

Here's why:

1. The mean is calculated by adding up all the values in a data set and then dividing by the number of values.

2. When the data is skewed, this means there are a few extremely high or low values.

3. These extreme values can greatly affect the total sum, and therefore, the mean.

4. For example, if we have the data set [1, 2, 3, 100], the mean would be 26.5, which is greatly affected by the value 100.

5. On the other hand, the median (the middle value when data is ordered from least to greatest) and the mode (the most frequently occurring value) are less affected by skewed data. In the above example, the median would be 2.5 and the mode would be whichever value appears most frequently.

6. Therefore, the mean is the measure of central tendency most affected by skewed data.