How to Solve for and Interpret z Scores – Introductory Statistics

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How to solve for and interpret z scores is covered in this video. Quantitative Specialists YouTube Channel: https://www.youtube.com/statisticsinstructor (or search for quantitative specialists)

Transcript of How to Solve for and Interpret z Scores – Introductory Statistics

  • 1. Finding the location of a score in a distribution Quantitative Specialists

2. Z score formula: Where: X = a raw score (a value on some variable, X ) = the population mean = the population standard deviation (Notice how both central tendency () and variability () are used to obtain a z score.) X z Quantitative Specialists 3. Indicate the number of standard deviations a score is away from the mean. Z-scores can be positive (above the mean), negative (below the mean), or zero (equal to the mean). Quantitative Specialists 4. Examples: z=+1; z=-2; z=0 z=+1; indicates that the score (X) is one standard deviation above the mean. z=2; indicates that a score (X) is two standard deviations below the mean. z=0; indicates that a score (X) is zero standard deviations away from the mean (it is equal to the mean). (Note: Non-integer z scores are possible as well, such a z = -.5.) Quantitative Specialists 5. Example: X = 110, = 100, = 10 Interpretation: A score (X) of 110 is 1 standard deviation above the mean of 100. 1 10 10 10 100110 z X z Quantitative Specialists 6. Example: X = 100, = 100, = 10 Interpretation: A score of 100 is 0 (zero) standard deviations away from the mean (it is equal to the mean). 0 10 0 10 100100 z X z Quantitative Specialists 7. Example: X = 90, = 100, = 10 Interpretation: A score of 90 is one standard deviation below the mean. 1 10 10 10 10090 z X z Quantitative Specialists 8. Example: X = 120, = 100, = 10 Interpretation: A score of 120 is two standard deviations above the mean. 2 10 20 10 100120 z X z Quantitative Specialists 9. Example: X = 95, = 100, = 10 Interpretation: A score of 95 is one-half (.5) of a standard deviation below the mean. 5. 10 5 10 10095 z X z Quantitative Specialists 10. For more statistics videos, check us out on YouTube: YouTube Channel: Quantitative Specialists https://www.youtube.com/statisticsinstructor (typing quantitative specialists in the search box will also find us) 11. 1. X = 58, = 50, = 10 2. X = 74, = 65, = 6 3. X = 47, = 50, = 5 4. X = 87, = 100, = 8 5. X = 22, = 15, = 5 6. X = 77, = 70, = 4 7. X = 41, = 50, = 10 X z Quantitative Specialists 12. 1. z = +.8 2. z = +1.5 3. X = -.6 4. X = -1.625 5. X = +1.4 6. X = +1.75 7. X = -.9 X z Quantitative Specialists 13. YouTube Channel: Quantitative Specialists https://www.youtube.com/statisticsinstructor (typing quantitative specialists in the search box will also find us)