{ Chapter 3 Lesson 9 Z-Scores

 Z-Score- The value z when you take an x value in the data set, subtract the mean from it, then divide by the standard deviation.  Raw Data- Data that has not been transformed or statistically manipulated, also called raw scores.  Standardized Data- Data that has been transformed into z-scores, also called standardized scores. Vocabulary

 A z-score tells you how many standard deviations the value is away from the mean and on which side of the mean it is on.  A positive z-score means the value is bigger than the mean (above)  A negative z-score means the value is smaller than the mean (below)  A z-score of 3 means that the number is 3 standard deviations above the mean  A z-score of means that the number is 2.25 standard deviations below the mean What does a Z-score tell you?

 If a data set has mean x and standard deviation s, the mean of the z- scores will be 0, and the standard deviation of the z-scores will be 1. Theorem

 Start with the data value  Subtract the mean from the value  Divide by the Standard Deviation How to Calculate a Z-Score

 Take the Z-score  Multiply it by the Standard Deviation  Add the mean How to Calculate Number from Z-score

 Data has a mean of 20 and a standard deviation of 4  What is the z-score of 18?  What is the z-score of 24?  What is the z-score of 20?  Which number has a z-score of 1.5 below the mean?  Which number has a z-score of 3 above the mean? Examples

 Consider a population of men with a mean weight of 200 pounds and a standard deviation of 20 pounds, and a population of women with a mean weight of 140 pounds and a standard deviation of 15 pounds.  Who is heavier relative to his or her population: a man who weighs 210 pounds of the woman who weighs 150 pounds? (look at the z-scores)  Suppose a woman in the population weighs 110 pounds, what would be the equivalent weight of a man in his population? (have same z-score) Example

 Worksheet 3-9 Homework