Frequency Distribution Graphs

In a frequency distribution graph, the score categories (X values) are listed on the x-axis (also called the abscissa), and the frequencies are listed on the y-axis (the ordinate). For scores that fall on an interval or ratio scale, a histogram or a polygon graph should be used. In a histogram, a bar is centered above each score (or interval) so that the height corresponds to the frequency of that score or interval and the width corresponds to the real limits of the score or interval. In a polygon, a dot is centered above each score so that the height of the dot corresponds to the frequency of the X value, and straight lines then connect the dots. At the ends, a line is drawn from the first X value with a frequency greater than zero to the first preceding or following X value for which the frequency is zero, so that the graph returns to zero at both ends.

For scores that fall on a nominal or ordinal scale, a bar graph should be used to display the data. A bar graph is similar to a histogram except that the width of the bars does not correspond to the real limits. Thus, the heights of bars correspond to the frequencies of the X values, but there is a gap between adjacent bars to indicate that the scale of measurement is not continuous.

Often, populations of interest are too large to know the exact frequencies of any of the specific categories (X values). In such a case, population distributions can be shown using relative frequency instead of the absolute number of individuals per category. If the scores are measured on an interval or ratio scale, the histogram and/or polygon used to display the data presents a smooth curve between the values rather than a jagged pattern, to reflect the fact that the distribution is not showing exact frequencies for each category but only estimations.

Central tendency is a term that refers to a set of measures that capture accurately the center of a distribution. As such, these measures provide information about an entire set of scores, condensed into one value. There are three different measures of central tendency that we will consider in this course, the mean, the median, and the mode. It is important to realize that although each of these measures concerns central tendency, they often take on different values for a given set of scores. This is because each of these measures is sensitive to aspects of the distribution, such as its shape.