Question

If five points were added to each score in a distribution, how would this change each of the following: the range, the mean, the median, the mode, the variance, the standard deviation?

Answer 1

Adding five points to each score in a distribution would increase the range, mean, median, variance, and standard deviation by five, but it would not change the mode.

Step-by-step explanation:

To understand how adding five points to each score in a distribution would change various measures, let's consider each one:

1. The range: The range is the difference between the highest and lowest scores. Adding five points to each score would increase the range by five, as both the highest and lowest scores would be five points higher.
2. The mean: The mean is the average of all the scores. Adding five points to each score would increase the mean by five, as each score is increased by five and the sum of the scores would also increase by five times the number of scores.
3. The median: The median is the middle value when the scores are arranged in order. Adding five points to each score would increase the median by five, as each score would be five points higher.
4. The mode: The mode is the most frequently occurring score. Adding five points to each score would not change the mode, as the relative frequencies of the scores would remain the same.
5. The variance: The variance measures the spread or dispersion of the scores. Adding five points to each score would increase the variance, as the individual scores are farther away from the new mean. The variance is calculated by summing the squared differences from the mean and dividing by the number of scores.
6. The standard deviation: The standard deviation is the square root of the variance. Adding five points to each score would increase the standard deviation, as the variance is higher.