Z-Score (Standard Score) Statistics Example 2

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

Example 2

hard
Alice scores 85 in Maths (ฮผ=75,ฯƒ=5\mu = 75, \sigma = 5) and 90 in English (ฮผ=80,ฯƒ=10\mu = 80, \sigma = 10). In which subject did she perform better relative to her class?

Solution

  1. 1
    Step 1: Maths z-score: z=85โˆ’755=2z = \frac{85-75}{5} = 2.
  2. 2
    Step 2: English z-score: z=90โˆ’8010=1z = \frac{90-80}{10} = 1.
  3. 3
    Step 3: Alice performed better in Maths (z = 2 vs z = 1) relative to her classmates.

Answer

Maths (z = 2 vs z = 1). She was further above the class mean in Maths.
Z-scores allow fair comparison across subjects with different means and standard deviations. A higher z-score indicates a relatively stronger performance.

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 3 medium

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

Example 4 medium

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

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