Chapter 22: Using Statistics to Describe Variables

Chapter 22: Using Statistics to Describe Variables

Complete Chapter Questions With Answers

Sample Questions Are Posted Below

4. Which of the following measures is the most helpful both for providing a quantification of dispersion and for providing a way to interpret how far away from the mean each individual score is?

ANS:  A

Measures of dispersion, such as the range, difference scores, variance, and standard deviation, provide important insight into the nature of the data. The standard deviation is an important statistic, both for understanding dispersion within a distribution and for interpreting the relationship of a particular value to the distribution.

DIF:    Cognitive Level: Analysis                REF:   Page 554

5. Which of the following measures is merely a simple difference score?

ANS:  A

The simplest measure of dispersion is the range. In published studies, range is presented in two ways: (1) the range is the lowest and highest scores, or (2) the range is calculated by subtracting the lowest score from the highest score. In this form, the range is a difference score that uses only the two extreme scores for the comparison. The range is generally reported in published studies but is not used in further analyses.

DIF:    Cognitive Level: Analysis                REF:   Page 554

6. The data set is: 2, 3, 6, 7, 12. A measure of dispersion is calculated, and it is about 3.5. What is this measure of dispersion?

ANS:  D

The definition of standard deviation (SD) is the average difference between the mean and each of the scores in the set. Standard deviation (SD) is a measure of dispersion that is the square root of the variance. SD is the most precise analysis technique for examining the distribution of scores. SD includes difference scores in its calculation but does not involve the use of standardized scores.

DIF:    Cognitive Level: Application           REF:   Page 555

7. The data set is as follows: Ford, Ford, Chevy, Toyota, Ford, Ford, Chevy, Dodge, Dodge, Dodge, Ford, Subaru, Chevy, Toyota, Chevy. What measures of central tendency and dispersion will be used with this set?

ANS:  D

The data are not inherently numerical in nature and represent only a nominal level of measurement. None of the listed measures of variability are suitable for nominal-level data. The mode is the only measure of central tendency appropriate for nominal data. The mode is the numerical value or score that occurs with the greatest frequency in a data set.

DIF:    Cognitive Level: Application           REF:   Page 552

8. Twenty student nurses take the NCLEX examination. If the average of the twenty scores is known, how many degrees of freedom are there in the sample?

ANS:  B

The concept of degrees of freedom was used originally in reference to computing a confidence interval, but it applies to any statistical computation. Degrees of freedom are the number of independent pieces of information that are free to vary in order to estimate another piece of information. If, for instance, the mean and the total “n” are known, if all of the values except one are known, the last one can be calculated. However, if all except two are known, one has the freedom to vary, and the other one’s value is then set. In calculations, the degrees of freedom (df) are n – 1. This means that there are n – 1 independent observations in the sample of n data points that are free to vary (to be any value).

DIF:    Cognitive Level: Application           REF:   Page 558