Z-Score (Standard Score) Statistics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
A data value has a z-score of โˆ’1.5-1.5. If the distribution has ฮผ=50\mu = 50 and ฯƒ=8\sigma = 8, find the original value.

Solution

  1. 1
    Step 1: Use x=ฮผ+zโ‹…ฯƒ=50+(โˆ’1.5)(8)x = \mu + z \cdot \sigma = 50 + (-1.5)(8).
  2. 2
    Step 2: x=50โˆ’12=38x = 50 - 12 = 38.

Answer

x=38x = 38
Rearranging the z-score formula lets us convert standardised scores back to original values, connecting abstract z-scores to real measurements.

About Z-Score (Standard Score)

A z-score tells you how many standard deviations a value is from the mean, calculated as z=xโˆ’ฮผฯƒz = \frac{x - \mu}{\sigma}. Positive z-scores are above the mean; negative z-scores are below. Z-scores allow comparison of values from different distributions.

Learn more about Z-Score (Standard Score) โ†’

More Z-Score (Standard Score) Examples

Example 1 medium

A student scores 78 on a test where [formula] and [formula]. Calculate her z-score and interpret it.

Example 2 hard

Alice scores 85 in Maths ([formula]) and 90 in English ([formula]). In which subject did she perform

Example 4 medium

In a class, test scores have mean [formula] and standard deviation [formula]. A student scores 55. F

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