Published on July 22, 2014
Finding the location of a score in a distribution Quantitative Specialists
Z score formula: Where: X = a raw score (a value on some variable, X ) µ = the population mean σ = the population standard deviation (Notice how both central tendency (µ) and variability (σ) are used to obtain a z score.) X z Quantitative Specialists
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
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
Example: X = 110, µ = 100, σ = 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
Example: X = 100, µ = 100, σ = 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
Example: X = 90, µ = 100, σ = 10 Interpretation: A score of 90 is one standard deviation below the mean. 1 10 10 10 10090 z X z Quantitative Specialists
Example: X = 120, µ = 100, σ = 10 Interpretation: A score of 120 is two standard deviations above the mean. 2 10 20 10 100120 z X z Quantitative Specialists
Example: X = 95, µ = 100, σ = 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
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)
1. X = 58, µ = 50, σ = 10 2. X = 74, µ = 65, σ = 6 3. X = 47, µ = 50, σ = 5 4. X = 87, µ = 100, σ = 8 5. X = 22, µ = 15, σ = 5 6. X = 77, µ = 70, σ = 4 7. X = 41, µ = 50, σ = 10 X z Quantitative Specialists
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
YouTube Channel: Quantitative Specialists https://www.youtube.com/statisticsinstructor (typing “quantitative specialists” in the search box will also find us)
z-Scores Reporting Category Statistics ... will interpret variation in real-world ... z-Scores; Statistics; ...
Probability and statistics ... Introduction to the normal distribution. ... ck12.org normal distribution problems: z-score.
Covers measures of position in statistics: ... Percentiles, Quartiles, z-Scores. ... Here is how to interpret z-scores.
Definition of z score, from the Stat Trek dictionary of statistical terms and concepts. This statistics glossary includes definitions of all technical ...
Calculating and Interpreting Z-Scores ... A z-score is used in statistics to model any normal distribution as a standard normal distribution.
Introduction to Probability and Statistics. ... To interpret the results of our RetroPsychoKinesis experiments, ... please visit the z Score Probability ...
This example shows how to find the z-score for a data point. ... Excel 2010 Statistics #34.5: Z-Score IF, Standard Deviation IF, Mean IF, ...
Find the z-score of a particular measurement given the mean and ... Khan Academy is a nonprofit with the mission of ... Inferential statistics ...
Analyzing and Interpreting Statistics ... contexts and calculate and interpret mean absolute deviation, standard deviation, and z‐scores. ...