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# Measures of Central Tendency for Numerical Data Study Guide (page 3)

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#### Example

Find the sample mean, sample median, and sample mode for the difference in the number of blinks while playing video games and the number of blinks during normal conversation. Which one do you think is the best measure of central tendency for these data?

#### Solution

The sample mean is the average of the sample values, that is, the average of the sample differences:

To find the median, we first order the sample values from smallest to largest:

13   13   17   17   18   19

21   24   26   26   27   29

32   34   40

Because there are 15 values in the sample, the middle value is the = 8th value in the list; that is, the sample median is 24.

The sample mode is the most frequently occurring value in the sample. Here, the values of 13, 17, and 26 were each observed twice. In these cases, the sample mode is of little value in measuring central tendency.

The mean and median provide good measures of the center of distribution, but the mode does not.

## Measures of Central Tendency for Numerical Data In Short

Mean, median, and mode are three measures of central tendency. Each provides a measure of the middle value in the population. The mean is the average of all population values. The median is the middle of the population values. The mode is the most frequently occurring population values. The sample mean, sample median, and sample mode are sample estimates of the corresponding population parameters.

Find practice problems and solutions for these concepts at Measures of Central Tendency for Numerical Data Practice Exercises.

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