Question

What are the minimum and maximum of the following dataset? Normalize these data so that the normalized data have a minimum of 0 and maximum of 1.
•   5.0, 5.5, 6.2, –4.8, 7.2, 5.4

Answer 1

The data in ascending order is:

Data

-4.8

5

5.4

5.5

6.2

7.2

The minimum value is -4.8

The maximum value is 7.2

Now normalizing the data, we need to find the mean and standard deviation.

The data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	-4.8	23.04
	5	25
	5.4	29.16
	5.5	30.25
	6.2	38.44
	7.2	51.84
Sum =	24.5	197.73

The sample mean is computed as follows:

Also, the sample variance is

Therefore, we get that the sample standard deviation is

With the sample mean and sample standard deviation calculated above, we can normalize the scores (which is, compute the z-scores)as shown in the table below:

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