Calculating Standardized Scores

1. Assume the arithmetic mean for a set of scores to be 50 and the standard deviation to be 5, calculate the z-score for scores of 65, 50, 45, and 60.

                                                        z-score computations

raw score of 65, z-score =

raw score of 50, z-score =

raw score of 45, z-score =

raw score of 60, z-score =
2. Assume the arithmetic mean for a set of raw scores on an IQ equivalent test to be 65 and the standard deviation to be 10. Calculate the z-score and then convert it into an IQ equivalent (Assuming the standardized mean for IQ is 100 and the standard deviation is 15). Calculate the IQ-score equivalents for raw scores of 80, 75, 65, and 50. Note: You are NOT being asked for the z-score.

                                                                IQ-score computation

raw score of 80, IQ-score =

raw score of 75, IQ-score =

raw score of 65, IQ-score =

raw score of 50, IQ-score =

3. Jann scored 50 on her math test and 80 on her science test. The class mean was 40 and the standard deviation was 5 on the math test. The class mean was 100 and the standard deviation was 10 on the science test. On which test did she perform better in relation to her peers and why?

4. Ramone scores 40 on his history test and 40 on his chemistry test. The class mean for both tests is 30. The standard deviation for the history test is 10 and the standard deviation for the chemistry test is 5. On which test did he do better in relation to his peers and why?

5. What are the mean, mode, median and standard deviation for the following population: 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 3, 4, 4, 5, 5, 5, and 6?

Mean=

Mode=

Median=

Standard Deviation=

6. What are the mean, mode, median and standard deviation for the following sample: 12, 13, 14, 15, 16, 16, 15, 14, 13, 14, 14, 15, and 14?

 Mean=

Mode=

Median=

Standard Deviation=

7. The following scores were recorded on a health test from an entire class with 24 students.  Use whatever skills you have to calculate the z-score for a raw score of 10. You need to determine whether to treat this as a sample or population.

6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 7, 8, 13, 12, 9, 11, 10, 12, 11, 10, 9, 10, 11, and 11.

z-score =

 

8. Assuming that you have a normal distribution, what percentage of students would have z-scores between 1.0 and 2.4? Use the area under the normal curve calculator to complete this problem: http://davidmlane.com/hyperstat/z_table.html