Variability and Standard Scores

1. If Q3 - Q2 is smaller than Q2 - Q1 what is the shape of the distribution?

2. A z-score is an index of variability expressed in units of the (?????) with a mean equal to (?????) and a standard deviation equal to (?????).

3. If one divides the sum of the squared deviations from the mean by the number of observations, the resultant is called what?

4. If the mean and standard deviation of a distribution are, respective, 18 and 2, what is the z-score value and what is the T-score value of the following raw scores?
a. 21
b. 18.5
c. 15

5. What is the relationship between the range and N? Why?

6. Given a distribution of scores, from what part of the distribution could you remove cases and thereby increase the standard deviation?

7. Given a distribution of scores, from what part of the distribution could you remove cases and thereby increase the mean and decrease the standard deviation simultaneously?
a.IQ of high school seniors vs IQ of college freshmen
Larger mean_____________
Larger standard deviation_____________
b. Strength of all college freshmen vs strength of only male college freshmen
Larger mean______________
Larger standard deviation_____________

8. If the mean on an examination is 16, the median is 14, and the standard deviation is 5 and we give each student a bonus of four points, the mean will become (?????), the median will become (?????) and the standard deviation will be (?????).

9. For each of the following examples, determine which will have a large mean and which a larger standard deviation.

10. Calculate the mean and standard deviation for the following scores:
12, 10, 4, 8, 5, 3, 1, 0, 2, 5, 5.

11. What are the standard score values (z and T) of the score of 1?

12. What is the raw score value of a standard score of 2? (z-score)

13. What is the raw score value of a standard score of 40? (T-score)

14. Two years ago a group of 12 year olds had a reading ability expressed by a mean score of 40 and a standard deviation of 4. The same students had a composition ability expressed by a mean of 60 and a standard deviation of 2. Today, the group has gained an average of 10 points in reading and an average of 6 points in composition. Use standard scores to decide which gain represents the greater increase.

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