How to Solve for and Interpret z Scores – Introductory Statistics

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Finding the location of a score in a distribution Quantitative Specialists

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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

Page 1: How to Solve for and Interpret z Scores – Introductory Statistics

Finding the location of a score in a distribution

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Page 2: How to Solve for and Interpret z Scores – Introductory Statistics

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.)

Xz

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Page 3: How to Solve for and Interpret z Scores – Introductory Statistics

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).

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Page 4: How to Solve for and Interpret z Scores – Introductory Statistics

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.)

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Page 5: How to Solve for and Interpret z Scores – Introductory Statistics

Example: X = 110, µ = 100, σ = 10

Interpretation: A score (X) of 110 is 1 standard deviation above the mean of 100.

110

10

10

100110

z

Xz

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Page 6: How to Solve for and Interpret z Scores – Introductory Statistics

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).

010

0

10

100100

z

Xz

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Page 7: How to Solve for and Interpret z Scores – Introductory Statistics

Example: X = 90, µ = 100, σ = 10

Interpretation: A score of 90 is one standard deviation below the mean.

110

10

10

10090

z

Xz

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Page 8: How to Solve for and Interpret z Scores – Introductory Statistics

Example: X = 120, µ = 100, σ = 10

Interpretation: A score of 120 is two standard deviations above the mean.

210

20

10

100120

z

Xz

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Page 9: How to Solve for and Interpret z Scores – Introductory Statistics

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

Xz

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Page 10: How to Solve for and Interpret z Scores – Introductory Statistics

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)

Page 11: How to Solve for and Interpret z Scores – Introductory Statistics

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

Xz

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Page 12: How to Solve for and Interpret z Scores – Introductory Statistics

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

Xz

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Page 13: How to Solve for and Interpret z Scores – Introductory Statistics

YouTube Channel: Quantitative Specialists

https://www.youtube.com/statisticsinstructor (typing “quantitative specialists” in the search box will also find us)