Z-Score (Standard Score) Statistics Example 4

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

Example 4

medium
In a class, test scores have mean ฮผ=65\mu = 65 and standard deviation ฯƒ=5\sigma = 5. A student scores 55. Find the z-score and interpret it.

Solution

  1. 1
    Step 1: Compute z=xโˆ’ฮผฯƒ=55โˆ’655=โˆ’2z = \frac{x-\mu}{\sigma} = \frac{55-65}{5} = -2.
  2. 2
    Step 2: A z-score of -2 means the score is 2 standard deviations below the mean.

Answer

z=โˆ’2z = -2, meaning the score is 2 standard deviations below the mean.
Z-scores standardize values so we can compare how far they are from the mean. Negative z-scores indicate values below the mean, while positive z-scores indicate values above it.

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 3 medium

A data value has a z-score of [formula]. If the distribution has [formula] and [formula], find the o

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