## Research Methods and Statistics A Critical Thinking Approach 4th International Edition – Test Bank

**Chapter 5**

**Data Organization and Descriptive Statistics**

**Chapter Outline**

Organizing Data

Frequency Distributions

Graphs

Bar Graphs and Histograms

Frequency Polygons

Descriptive Statistics

Measures of Central Tendency

Mean

Median

Mode

Measures of Variation

Range

Average Deviation and Standard Deviation

Types of Distributions

Normal Distributions

Kurtosis

Positively Skewed Distributions

Negatively Skewed Distributions

z-scores

z-scores, the Standard Normal Distribution, Probability, and Percentile Ranks

Summary

**Review of Key Terms**

**Average Deviation—**An alternative measure of variation that, like the standard deviation, indicates the average difference between the scores in a distribution and the mean of the distribution.

**Bar Graph—**A graphical representation of a frequency distribution in which vertical bars are centered above each category along the x-axis and are separated from each other by a space indicating that the levels of the variable represent unrelated and distinct categories.

**Class Interval Frequency Distribution—**A table in which the scores are grouped into intervals and listed along with the frequency of scores in each interval.

**Descriptive Statistics—**Numerical measures that describe a distribution by providing information on the central tendency of the distribution, the width of the distribution, and the shape of the distribution.

**Frequency Distribution—**A table in which all of the scores are listed along with the frequency with which each occurs.

**Frequency Polygon— **A line graph of the frequencies of individual scores.

**Histogram—** A graphical representation of a frequency distribution in which vertical bars centered above scores on the x-axis touch each other to indicate that the scores on the variable represent related, increasing values.

**Kurtosis—**How flat or peaked a normal distribution is.

**Leptokurtic—**Normal curves that are tall and thin with only a few scores in the middle of the distribution having a high frequency.

**Mean—**A measure of central tendency; the arithmetic average of a distribution.

**Measure of Central Tendency—**A number intended to characterize an entire distribution.

**Measure of Variation—** A number that indicates how dispersed scores are around the mean of the distribution.

**Median—**A measure of central tendency; the middle score in a distribution after the scores have been arranged from highest to lowest or lowest to highest.

**Mesokurtic**—Normal curves that have peaks of medium height and distributions that are moderate in breadth.

**Mode**—A measure of central tendency; the score in a distribution that occurs with the greatest frequency.

**Negatively Skewed Distribution—**A distribution in which the peak is to the right of the center point and the tail extends toward the left, or in the negative direction.

**Normal Curve**—A symmetrical, bell-shaped frequency polygon representing a normal distribution.

**Normal Distribution—**A theoretical frequency distribution having certain special characteristics.

**Percentile Rank—**A score that indicates the percentage of people who scored at or below a given raw score.

**Platykurtic**—Normal curves that are short and more dispersed (broader).

**Positively Skewed Distribution— **A distribution in which the peak is to the left of the center point and the tail extends toward the right, or in the positive direction.

**Probability**—The expected relative frequency of a particular outcome.

**Qualitative Variable—**A categorical variable for which each value represents a discrete category.

**Quantitative Variable—**A variable for which the scores represent a change in quantity.

**Range**—A measure of variation; the difference between the lowest and the highest score in a distribution.

**Standard Deviation—**A measure of variation; the average difference between the scores in the distribution and the mean or central point of the distribution, or more precisely, the square root of the average squared deviation from the mean.

**Standard Normal Distribution—**A normal distribution with a mean of 0 and a standard deviation of 1.

**Variance—**The deviation squared.

** z-score (Standard Score)—**A number that indicates how many standard deviation units a raw score is from the mean of a distribution.

**Relevant Articles from Handbook for Teaching Statistics and Research Methods (1st ed.)**

Beins, B. Teching the relevance of statistics through consumer-oriented research. Pp. 5-6.

Dillbeck, M. C. Teaching statistics in terms of the knower. Pp. 20-23.

Dillon, K. M. Statisticophobia. P. 3.

Forsyth, G. A. A task-first individual-differences approach to designing a statistics and methodology course. Pp. 15-17.

Hastings, M. W. Statistics: Challenge for students and the professor. Pp. 6-7.

Jacobs, K. W. Instructional techniques in the introductory statistics course: The first class meeting. P. 4.

Magnello, M. E., & Spies, C. J. Using organizing concepts to facilitate the teaching of statistics. Pp. 12-15.

Shatz, M. A. The Greyhound strike: Using a labor dispute to teach descriptive statistics. P. 35.

Ward, E. F. Statistics mastery: A novel approach. Pp. 17-20.

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