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 * Aim:** How do z-scores help us to compare different data sets?

At the end of this lesson, you will be able to...
 * 1) define a z-score
 * 2) compute the z-score for a data value
 * 3) use the z-scores for individual data points to compare percentile ranks in different data sets
 * 4) use z-scores in real world problems

These videos will show you hoe to compare different sets of data, for example two sets of tests with different means and standard deviations.

Before you watch the videos, copy down the following questions into your notebooks then answer them as you watch the videos.


 * 1) What is a z-score?
 * 2) What is the formula for finding a z-score? This formula is not given on the Regents Reference sheet
 * 3) What does a positive z-score mean?
 * 4) What does a negative z-score mean?
 * 5) When comparing z-scores is a higher z-score better or worse than a lower z-score? Explain.
 * 6) How are z-scores helpful when looking at two different sets of data?

media type="youtube" key="Wp2nVIzBsE8" width="425" height="350"
 * This video shows how to compute z-scores**

media type="youtube" key="fFFJr5AbjPI" width="425" height="350"
 * This video shows how to compare z-scores and their interpretations**

1. On a standardized test, the test scores are normally distributed with a mean of 60 and a standard deviation of 6. a. Of the data, 84% of the scores are at or below what score? (Ans: 66) b. Of the data, 16% of the scores are at or below what score? (Ans: 54) c. What is the z-score of a score of 48? (Ans: -2) d. If 2000 students took the test, how many would be expected to score at or below 24? (Ans: 50)
 * Classwork:** Complete each of the following:

2. For a normal distribution of weights, the mean weight is 160 pounds and a weight of 168 pounds has a z-score of 2. a. What is the standard deviation of the set of data? (Ans: 13) b. What percent of the weights are between 155 and 165? (Ans: About 30%)


 * Homework:** complete #3-10, 11 - 19 odd

[|z-scores_1.JPG]

[|z-scores_2.JPG]


 * Answers:**

[|A-z_scores.JPG]


 * Journal entry:** The mean of a math test and for a science test were each 80. The standard deviation of the math test was three and of the science test was five. If Beverly had an 87 on each test, in which class did she do better when compared to her classmates? Explain your answer. Use video 2 to help you.