# How to Solve for and Interpret z Scores – Introductory Statistics

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Published on July 22, 2014

Author: quantitative_specialists

Source: slideshare.net

## Description

How to solve for and interpret z scores is covered in this video.

Quantitative Specialists
(or search for quantitative specialists)

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)

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