Читать книгу Student Study Guide to Accompany Statistics Alive! - Wendy J. Steinberg - Страница 17

1 They provide a single score to represent an entire set of numbers. They provide a quick “snapshot” of where the majority of the scores are located.

2 This indicates that the single score allows you to have a better understanding of where the majority of the scores from a data set are located.

3 The mode is the most commonly occurring score. It is not a very stable measure of central tendency because the addition of a few scores can drastically change the location of the mode. For example, a data set may have a mode of 3. However, after adding a few scores with the value of 15, the mode may become 15.

4 The median is the center score, or the score that occurs at the 50th percentile. It is not very sensitive to changes in a data set. In large data sets, a large number of scores would need to be added to heavily influence the median.

5 The mean differs from the median and mode in that it includes every score in its calculation. This makes it far more sensitive to changes in the data set than the other measures of central tendency.

6 This indicates that the total distance from the mean of scores above the mean is equal to the total distance from the mean of scores below the mean. This indicates that if you were to subtract the mean from each of the scores (X − M), the absolute value of the sum of these differences for the scores above the mean will be equal to the absolute value of the sum of these differences for the scores below the mean.

7 The mean includes all of the scores in the distribution in its calculation. If you were to add any score to a data set (other than a score that is the mean itself), the mean would change, whereas this may not be the case with the other measures of central tendency.

8 An outlier is an extreme score, or a score that differs greatly from all other scores. For example, when assessing the batting average of an entire baseball team, a very good player could drastically improve the average, whereas a very poor player could lower the average. The median would be a more appropriate measure of central tendency.

9 In a positively skewed distribution, you can expect the mode to be the smallest value, followed by the median, and the mean would be the largest value. In a negatively skewed distribution, the mean would be the smallest value, followed by the median, and finally the mode. In a symmetrical distribution, all three measures are equal.

10 The median would be the most appropriate because the mean is being pulled in the direction of the tail. The mode “ignores” the fact that the distribution is skewed by reporting the most commonly occurring score. The median, however, falls between these scores and so is the most appropriate.

11 You should report the mode because that will be the largest value.

12 You could report any measure because all three would be equal.

13 This should have no influence on the measures of central tendency because the data are normally distributed.