# Measure of Central Tendency

1. What information does each measure of central tendency provide?

2. Why are measures of variability essential statistical tools for describing behavior?

3. How do standard scores assist you in determining relative standing and in making comparisons between groups?

4. What happens to the mean in a skewed distribution? What happens to the median?

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#### Solution Preview

1. What information does each measure of central tendency provide?

The three most commonly used measures of the center of the data are the mode, mean and median.

The mean is the sum of the values of the observations divided by the number of observations. The median is the midpoint of the observations, when arranged in order. Half of the observations in a data set lie below the median and half lie above the median. The mode is the most frequent value. It is the value that occurs most commonly in the data set.

Measures of central tendency do two jobs:

(1) Provide a summary of large amounts of data

(2) By providing common ground that lets us easily compare groups

Mode

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The mode is the least restricted measure of central tendency and is appropriate for use with all levels of measurement. The mode is simply the value that occurs most often in the data.

Median

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The median is the point in the distribution where 50% of the scores fall below it and 50% of the scores fall above it. The median is often the best measure of central tendency in distributions that are asymmetrical (skewed). To determine the median, arrange the scores from least to greatest. If there are an odd number of scores, then the median is the score in the middle. In the scores 2, 3, 4, 5, 6, the median is 4 because it is the middle score. If an even ...

#### Solution Summary

Measures of Central Tendency are explained.