Z-Score (Standard Score) Statistics Example 1

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Example 1

medium
A student scores 78 on a test where ฮผ=70\mu = 70 and ฯƒ=4\sigma = 4. Calculate her z-score and interpret it.

Solution

  1. 1
    Step 1: z=xโˆ’ฮผฯƒ=78โˆ’704=2z = \frac{x - \mu}{\sigma} = \frac{78 - 70}{4} = 2.
  2. 2
    Step 2: A z-score of 2 means the student scored 2 standard deviations above the mean.
  3. 3
    Step 3: By the empirical rule, only about 2.5% of students scored higher.

Answer

z=2z = 2. The student scored 2 standard deviations above the mean.
Z-scores standardise values to a common scale, telling us how many standard deviations a value is from the mean. This allows comparison across different distributions.

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 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

Example 4 medium

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

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