   Chapter 4, Problem 12P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

The range is completely determined by the two extreme scores in a distribution. The standard deviation, on the other hand, uses every score. a. Compute the range (choose either definition) and the standard deviation for the following sample of n = 5 scores. Note that there are three scores clustered around the mean in the center of the distribution, and two extreme values. Scores:     0    6    7    8    14 a. Now we break up the cluster in the center of the distribution by moving two of the central scores out to the extremes. Once again compute the range and the standard deviation. New scores:    0    0    7    14    14 a. According to the range, how do the two distributions compare in variability? How do they com­pare according to the standard deviation?

a.

To determine

To find: The range, variance and standard deviation for the sample scores.

Explanation

Given info:

The data represents the sample scores. The scores are 0, 6, 7, 8 and 14.

Calculation:

First case of range:

Range=XmaxXmin

The range for the sample of scores is,

From the sample of scores it can be observed that the maximum and minimum values of scores are 14 and 0.

Range = XMaxXMin=140=14

Thus, the range for the sample of scores is 14.

Second case of range:

The second case for range is used, in case of whole numbers.

The general formula for range of whole numbers is,

Range=XmaxXmin+1

If the scores are whole numbers the range is,

Range=XmaxXmin+1=110+1=15

Thus, the range for the sample of scores is 15

(b)

To determine

To find: The range and standard deviation for the sample scores of two spreading scores in the middle.

c.

To determine

To compare: The variability of two distributions by using the range.

To compare: The variability of two distributions by using the standard deviation.

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