1. STANDARDIZED VALUES: LESSON 21

2. HOW CAN YOU USE STANDARDIZED VALUES TO COMPARE VALUES FROM TWO DIFFERENT NORMAL DISTRIBUTIONS? STANDARDIZED VALUE TELLS HOW MANY STANDARD DEVIATIONS A GIVEN VALUE LIES FROM THE MEAN OF A DISTRIBUTION.

3. FACTS: 1.Standardized values are sometimes called z-scores. 2.If the standardized value is positive, the value lies above the mean. 3.If the standardized value is negative, the value lies below the mean.

4. EXAMPLE: Jake earned a grade of 50 on a normally distributed test with a mean 45 and standard deviation 10. On another normally distributed test with mean 70 and standard deviation 15, he earned a 78.

6. Jake’s standardized value and percentile ranking are higher for the second test. So Jake did better on it, relative to the other students.

7. 1.Examine the table below, which gives information about the heights of young Americans aged 18 to 24. Each distribution is approximately normal. Heights of American Young Adults (in inches) MENWOMEN 68.565.5 2.72.5

8. a.Sketch the two distributions. Include a scale on the horizontal axis. b.Alexis is 3 standard deviations above average in weight. How tall is he? c.Marvin is 2.1 standard deviations below average in height. How tall is he?

9. d.Miguel is 74” tall. How many standard deviations above average height is he? e.Jackie is 62” tall. How many standard deviations below average height is she? f.Marina is 68” tall. Steve is 71” tall. Who is relatively taller for her or his gender. Marina or Steve?

10. 1.Heights of American Young Adults (in inches) a.

11. b.65.5” + 3(2.5”) = 73” c.68.5” – 2.1(2.7”) = 62.83” d.74 – 68.5 = 2.04standard 2.7deviations above average e.62 – 65.5 = -1.4, or 1.4 standard 2.5 deviations below average

13. Marina is relatively taller than Steve because her height is farther above the mean as measured by the standard deviation for the appropriate distribution.

14. 2.Look more generally at how standardized values are computed. a.Refer to Problem 1, Parts d and e. Compute the standardized values for Miguel’s height and for Jackie’s height. 3.Now consider how standardizing values can help you make comparisons.

15. 3.Now consider how standardizing values can help you make comparisons. Refer to the table in Problem 1. Heights of American Young Adults (in inches)

16. a.Find the standardized value for the height of a young woman who is 5 feet tall. b.Find the standardized value for the height of a young man who is 5 feet 2 inches tall. c.Is the young woman in Part a or the young man in Part b shorter, relative to his or her own gender? Explain your reasoning.

18. c.The young man is relatively shorter because he is farther below the mean of his distribution as measured by the standard deviation than the young woman is from the mean of her distribution.

19. Homework 1.“Standardized Values” worksheet. 2.“Standardized Values” quiz.