Z-Score Math Example 3

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

Example 3

easy
A data point has value 4545 in a distribution with ฮผ=50\mu = 50 and ฯƒ=4\sigma = 4. Find its z-score.

Solution

  1. 1
    z=45โˆ’504=โˆ’54=โˆ’1.25z = \frac{45 - 50}{4} = \frac{-5}{4} = -1.25.
  2. 2
    The negative sign indicates the value is below the mean.

Answer

z=โˆ’1.25z = -1.25
A negative z-score means the data point is below the mean. The magnitude tells us it is 1.251.25 standard deviations below.

About Z-Score

A z-score measures how many standard deviations a data value is above or below the mean: z=(xโˆ’ฮผ)/ฯƒz = (x - \mu)/\sigma.

Learn more about Z-Score โ†’

More Z-Score Examples

Example 1 easy

A student scored [formula] on an exam where the mean was [formula] and the standard deviation was [f

Example 2 medium

On Test A, Maria scored [formula] ([formula], [formula]). On Test B, she scored [formula] ([formula]

Example 4 medium

In a class, test scores have mean [formula] and standard deviation [formula]. What raw score corresp

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