Читать книгу Student Study Guide to Accompany Statistics Alive! - Wendy J. Steinberg - Страница 29

1 Dispersion is important because it indicates the extent to which scores cluster around the mean or are very distant from the mean. This will help you determine how viable the mean is as a single descriptor of the data set. For example, a 0 to 10 scale with a mean of 5 and a standard deviation of 1 indicates that, on average, a score will deviate 1 point from the mean. This suggests that the majority of scores will fall between 4 and 6, making the mean a very good descriptor. However, if the mean is 5 and the standard deviation is 5, it means that the average deviation from the mean is 5 points, indicating that the scores fall everywhere on the scale.

2 The range does not consider all of the scores in the distribution. Also, it can be heavily influenced by extreme scores (drastically different upper or lower scores), and it is unaffected by the addition of nonextreme scores (scores that are not the upper or lower limits).

3 First, the deviation scores must be found. Then these scores must be squared. The squared deviation scores are then summed. Finally, this summed squared deviation score is divided by N or by n − 1.

4 This is because the deviation scores will sum to 0, which would indicate that there is no variability in the sample. Squaring the deviation scores creates a positive sum.

5 Variance is in area units. The standard deviation is in linear units. The difference is that the area units are squared, meaning one cannot apply them directly to the original scale of measurement. The linear units are in the same metric as the original scale.

6 Area units are changed to linear units by taking the square root of the area unit.

7 Deviation scores always sum to 0 because they represent each score’s numerical distance from the mean. Because the mean is the numerical center of the distribution, the distance of scores above the mean will always equal the distance below the mean.

8 This person would be considered an outlier because he or she falls so far away from the mean.

9 The range would not be affected at all by adding scores to the center of the distribution. However, the variance and standard deviation would become smaller.

10 This means that the values all fall on the same scale. The standard deviation is on the scale of the normal curve, which has unique properties that we will encounter in later modules.

11 The standard deviation represents the standardized average deviation that is applicable to the normal curve. The mean absolute deviation uses the absolute value of the deviation scores.

12 The mean absolute deviation does not fall within known places on the normal curve, which is extremely useful in the practice of statistics. Because of this, the mean absolute deviation is not commonly used.