Question

Assume the following 5 scores represent a sample: 2, 3, 5, 5, 6. Transform these scores into z-scores. Show all steps

Answer 1

The z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

How to transform the scores?

The sample scores are given as:

2, 3, 5, 5, 6.

Calculate the mean and the standard deviation using a statistical calculator.

From the statistical calculator, we have:

$\bar x = 4.2$ --- mean

$\sigma_x = 1.64$ --- standard deviation

The z-score is then calculated using

$z= \frac{x - \bar x}{\sigma}$

Where:

x = 2, 3, 5, 5, 6.

So, we have:

$z_1= \frac{2 - 4.2}{1.64} = -1.34$

$z_2= \frac{3 - 4.2}{1.64} = -0.73$

$z_3= \frac{5 - 4.2}{1.64} = 0.48$

$z_4= \frac{5 - 4.2}{1.64} = 0.48$

$z_5= \frac{6 - 4.2}{1.64} = 1.10$

Hence, the z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

Read more about z-scores at:

brainly.com/question/25638875

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