2.5/5.1 P & S: z-scores & percentiles review

Adam's Z-score on a test is +2.50. What does this mean?

• Adam's score has a 2.5% chance of being better than any other randomly selected score.

• Adam's test score was better than 25% of his peers.

• He scored 2.5 standard deviations above the average.

• He did terrible.

Joanne's score on a test gives her a Z-score is -1.50. What does this mean?

• Joanne didn't take the test yet.

• Joanne's test score is 1.50 standard deviations below the average test score.

• Joanne did better than 1.50 times her peers.

• Joanne's test score, on average, was 1.5 points lower than the other test scores.

What is the Z-score for Tina if she got a 31 on the ACT, the mean was 23 and the SD was 4?

• +0.20

• +2.00

• -2.00

• -0.20

So if Tina's Z-score is +2.00 and Paula's Z-score is +1.09, who performed better?

• Tina's performance is farther above the mean so she did better.

• Paula's score is closer to the mean so she did better.

• They both did the same.

What shape is the dot plot for SUV's?

• skewed right

• skewed left

• symmetrical

• none of the above

In Exercises 1 – 4, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What score represents the 70^th percentile? How should you interpret this?

In Exercises 1 – 4, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

Which score represents the 40^th percentile? How should you interpret this?

In Exercises 1 – 4, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What percentile is a score of 140? How should you interpret this?

In Exercises 1 – 4, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What percentile is a score of 170? How should you interpret this?

The distribution of the ages of the winners of the Tour de France from 1903 to 2016 is approximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.3 years. In Exercises 8 – 10, use the corresponding z-score to determine whether the age is unusual. Explain your reasoning. (Source:  Le Tour de France)

Winner:  Jan Ullrich           Age: 24