standard scores

Mirasol S. Madrid III-9 BS Psychology

Also called as z scores

Measures the difference

between the raw score and the

mean of the distribution using

standard deviation of the

distribution as a unit of

measurement

Reflects how many

standard deviations above

or below the mean a raw

score is

By itself, a raw score or X value provides very little information about how that particular score compares with other values in the distribution.

A score of X = 53, for example, may be a relatively low score, or an average score, or an extremely high score depending on the mean and standard deviation for the distribution from which the score was obtained.

50 60 70 80403020

0 1 2 3-1-2-3

x

z

If the raw score is transformed into a z-score, however, the value of the z-score tells exactly where the score is located relative to all the other scores in the distribution.

𝑧 =(𝑥 − 𝑥)

𝑠Where:

Z = standard score/z-score

X = Raw Score

𝒙 = Mean

S = Standard Deviation

𝑧 =(𝑥 − 𝜇)

𝜎Where:

Z = standard score/z-score

X = Raw Score

𝝁 = Mean

𝝈 = (sigma) Standard Deviation

Z-scores can be positive (above the mean), negative (below the mean), or zero (equal to the mean)

In a distribution of statistic test score,

having the mean of 75 and a standard deviation

of 10, find the z score, scoring 85

X = 85

𝑥 = 75

S = 10

1. Step 1

𝑧 =(85 − 75)

102. Step 2

𝑧 =(10)

10z = 1

A score of 85 is one (1)

standard deviation

above the mean

Find the Z score of 60

having a mean of 75

and a standard

deviation of 10

X = 60

𝑥 = 75

S = 10

1. Step 1

𝑧 =(55 − 75)

102. Step 2

𝑧 =(−20)

10z= -2

A score of 60 is two (2)

standard deviation

below the mean

X = 100

𝑥 = 100

S = 10

1. Step 1

𝑧 =(100 − 100)

102. Step 2

𝑧 =(0)

10z= 0

A score of 100 is falls

on the given mean.

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

1. z = +.8

2. z = +1.5

3. z = -.6

4. z = -1.625

5. z = +1.4