Activity 2: Finding z-scores There are two mathematical operations used when calculating a z-score: a. First, we take each score, and the mean (remember the mean was 80). Fill in the table and then make a dotplot for each. SCORE 61 65 65 73 75 77 78 78 79 80 80 80 80 81 81 88 89 93 98 99 SCORE - MEAN Dotplot for SCORE Dotplot for SCORE - MEAN 60 70 80 90 10 What happens to the shape, center, and variability when you subtract the mean from each score? b. Second, we take the SCORE - MEAN and by the standard deviation (remember the standard deviation is 10). Fill in the table and then make a dotplot. SCORE - MEAN - 19 -15 - 15 - 7 - 5 - 3 - 2 - 2 -1 0 0 0 0 1 1 8 9 13 18 19 SCORE - MEAN SD Dotplot for SCORE - MEAN SD 1 What happens to the shape, center, and variability when you divide by the standard deviation for each value? Summarize: What happens to the shape, center and variability of a distribution when you ..add or subtract the same value a from each value? ...multiply or divide by the same value b from each value? * *What is the mean and standard deviation of the distribution of z-scores? Will this be true for any distribution of z-scores? Explain