Psychology
Frequency Distribution
Frequency distribution in psychology refers to a table or graph that displays the frequency of various outcomes in a dataset. It shows how often each different value occurs in a set of data, providing a visual representation of the distribution of scores. This tool helps psychologists understand the patterns and variability within their data.
Written by Perlego with AI-assistance
Related key terms
1 of 5
8 Key excerpts on "Frequency Distribution"
eBook - PDF- Frederick Gravetter, Larry Wallnau(Authors)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
The immediate problem for the researcher is to organize the scores into some comprehensible form so that any patterns in the data can be seen easily and communicated to others. This is the job of descriptive statistics: to simplify the organization and presentation of data. One of the most common procedures for organizing a set of data is to place the scores in a Frequency Distribution . A Frequency Distribution is an organized tabulation of the number of individuals located in each category on the scale of measurement. A Frequency Distribution takes a disorganized set of scores and places them in order from highest to lowest, grouping together individuals who all have the same score. If the highest score is X = 10, for example, the Frequency Distribution groups together all the 10s, then all the 9s, then the 8s, and so on. Thus, a Frequency Distribution allows the researcher to see “at a glance” the entire set of scores. It shows whether the scores are generally high or low, whether they are concentrated in one area or spread out across the entire scale, and generally provides an organized picture of the data. In addition to providing a picture of the entire set of scores, a Frequency Distribution allows you to see the location of any individual score relative to all of the other scores in the set. A Frequency Distribution can be structured either as a table or as a graph, but in either case, the distribution presents the same two elements: 1. The set of categories that make up the original measurement scale. 2. A record of the frequency, or number of individuals in each category. Thus, a Frequency Distribution presents a picture of how the individual scores are dis-tributed on the measurement scale—hence the name Frequency Distribution. ■ ■ Frequency Distribution Tables The simplest Frequency Distribution table presents the measurement scale by listing the different measurement categories ( X values) in a column from highest to lowest.
- Theodore Coladarci, Casey D. Cobb(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
PART 1 Descriptive Statistics CHAPTER 2 Frequency Distributions 2.1 Why Organize Data? You perhaps are aware by now that in statistical analysis one deals with groups, often large groups, of observations. These observations, or data, occur in a variety of forms, as you saw in Chapter 1. They may be quantitative data, such as test scores, socioeconomic status, or per-pupil expenditures; or they may be qualitative data as in the case of sex, ethnicity, or favorite tenor. Regardless of their origin or nature, data must be organized and summarized in order to make sense of them. For taken as they come, data often present a confusing picture. The most fundamental way of organizing and summarizing statistical data is to construct a Frequency Distribution. A Frequency Distribution displays the differ- ent values in a set of data and the frequency associated with each. This device can be used for qualitative and quantitative variables alike. In either case, a Frequency Distribution imposes order on an otherwise chaotic situation. Most of this chapter is devoted to the construction of Frequency Distributions for quantitative variables, only because the procedure is more involved than that associated with qualitative variables (which we take up in the final section). 2.2 Frequency Distributions for Quantitative Variables Imagine that one of your professors, Dr. Casteñeda, has scored a multiple-choice exam that he recently gave to the 50 students in your class. He now wants to get a sense of how his students did. Simply scanning the grade book, which results in the unwieldy display of scores in Table 2.1, is of limited help. How did the class do in Table 2.1 Scores from 50 Students on a Multiple-Choice Examination 75 89 57 88 61 90 79 91 69 99 83 85 82 79 72 78 73 86 86 86 80 87 72 92 81 98 77 68 82 78 82 84 51 77 90 70 70 88 68 81 78 86 62 70 76 89 67 87 85 80 14
eBook - PDF- Robert S. Witte, John S. Witte(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
Your initial responsibility is to describe the data as clearly, completely, and concisely as possible. Statistics supplies some tools, including tables and graphs, and some guidelines. Beyond that, it is just the data and you. There is no single right way to describe data. Equally valid descriptions of the same data might appear in tables or graphs with different formats. By following just a few guidelines, your reward will be a well-summarized set of data. TABLES (Frequency DistributionS) 2.1 Frequency DistributionS FOR QUANTITATIVE DATA Table 2.1 shows one way to organize the weights of the male statistics students listed in Table 1.1. First, arrange a column of consecutive numbers, beginning with the light- est weight (133) at the bottom and ending with the heaviest weight (245) at the top. (Because of the extreme length of this column, many intermediate numbers have been omitted in Table 2.1, a procedure never followed in practice.) Then place a short verti- cal stroke or tally next to a number each time its value appears in the original set of data; once this process has been completed, substitute for each tally count (not shown in Table 2.1) a number indicating the frequency ( f ) of occurrence of each weight. A Frequency Distribution is a collection of observations produced by sorting obser- vations into classes and showing their frequency ( f ) of occurrence in each class. When observations are sorted into classes of single values, as in Table 2.1, the result is referred to as a Frequency Distribution for ungrouped data. Not Always Appropriate The Frequency Distribution shown in Table 2.1 is only partially displayed because there are more than 100 possible values between the largest and smallest observa- tions. Frequency Distributions for ungrouped data are much more informative when the number of possible values is less than about 20. Under these circumstances, they are a straightforward method for organizing data.
eBook - PDF- Lorena Madrigal(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
Most anthropology students are in the field or in the lab entering data (from hormonal analysis of urine samples to display behavior in non-human primates to number of projectile points in an archaeological site) with a computer next to them. Once they enter the data into the computer, these students will proceed to compute statistics with the same computer. Therefore, the need to explain how to compute a Frequency Distribution of continuous data as an intermediate stage in the computation of statistics, in my opinion, has disappeared. 16 The first step in data analysis Table 2.3 Raw data and Frequency Distribution of height in ten subjects (ungrouped data). Raw data Observation Height 1 179.58065582 2 156.68456038 3 161.43566923 4 156.49174451 5 138.00431500 6 164.41657784 7 170.25923455 8 163.65883671 9 157.44467354 10 156.41354636 Frequency Distribution Cumulative Cumulative Height Frequency Percent frequency percent 138.00431500 1 10.00 1 10.00 156.41354636 1 10.00 2 20.00 156.49174451 1 10.00 3 30.00 156.68456038 1 10.00 4 40.00 157.44467354 1 10.00 5 50.00 161.43566923 1 10.00 6 60.00 163.65883671 1 10.00 7 70.00 164.41657784 1 10.00 8 80.00 170.25923455 1 10.00 9 90.00 179.58065582 1 10.00 10 100.00 Table 2.4 A Frequency Distribution of height in 100 subjects. Cumulative Cumulative Height Frequency Percent frequency percent 123–132 1 1.00 1 1.00 133–142 5 5.00 6 6.00 143–152 17 17.00 23 23.00 153–162 39 39.00 62 62.00 163–172 29 29.00 91 91.00 173–182 8 8.00 99 99.00 183–192 1 1.00 100 100.00 If you do want to compute a Frequency Distribution using a computer program to display your data, you will need to tell the program how to group the subjects. Therefore, you need to declare that you want subjects grouped in five-year or ten-year categories, for example. You should make sure, of course, that you check that every subject has been assigned to one category. For example, when I constructed the Frequency Distribution
eBook - PDFBiostatistics
Basic Concepts and Methodology for the Health Sciences, 10th Edition International Student Version
- Wayne W. Daniel, Chad L. Cross(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
When we do this for our example, we have Table 2.3.1. A table such as Table 2.3.1 is called a Frequency Distribution. This table shows the way in which the values of the variable are distributed among the specified class intervals. By consulting it, we can determine the frequency of occurrence of values within any one of the class intervals shown. Relative Frequencies It may be useful at times to know the proportion, rather than the number, of values falling within a particular class interval. We obtain this information by dividing the number of values in the particular class interval by the total number of values. If, in our example, we wish to know the proportion of values between 50 and 59, inclusive, we divide 70 by 189, obtaining .3704. Thus we say that 70 out of 189, or 70/189ths, or .3704, of the values are between 50 and 59. Multiplying .3704 by 100 gives us the percentage of values between 50 and 59. We can say, then, that 37.04 percent of the subjects are between 50 and 59 years of age. We may refer to the proportion of values falling within a class interval as the relative frequency of occurrence of values in that interval. In Section 3.2 we shall see that a relative frequency may be interpreted also as the probability of occurrence within the given interval. This probability of occurrence is also called the experimental probability or the empirical probability . TABLE 2.3.1 Frequency Distribution of Ages of 189 Subjects Shown in Tables 1.4.1 and 2.2.1 Class Interval Frequency 30–39 11 40–49 46 50–59 70 60–69 45 70–79 16 80–89 1 Total 189 24 CHAPTER 2 STRATEGIES FOR UNDERSTANDING THE MEANINGS OF DATA In determining the frequency of values falling within two or more class intervals, we obtain the sum of the number of values falling within the class intervals of interest. Similarly, if we want to know the relative frequency of occurrence of values falling within two or more class intervals, we add the respective relative frequencies.
- Kenneth Meier, Jeffrey Brudney, John Bohte, , Kenneth Meier, Jeffrey Brudney, John Bohte(Authors)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 70 Chapter 4 Frequency Distributions Clearly, presenting these data in their raw form would tell the administrator little or nothing about trash collection in Normal. For example, how many tons of trash do most teams collect? Do the teams seem to collect about the same amount of trash, or does their performance vary? The most basic restructuring of raw data to facilitate understanding of what they mean is the Frequency Distribution . A Frequency Distribution is a table that pairs data values—or ranges of data values—with their frequency of oc-currence. For example, Table 4.1 is a Frequency Distribution of the number of arrests each Morgan City police officer made in March 2014. Note that the entire table is labeled, as is each column. Here, the data values are the number of arrests, and the frequencies are the number of police officers. This procedure makes it easy to see that most Morgan City police officers made between 16 and 20 arrests in March 2014. Public and nonprofit managers use a standard vocabulary to describe data. A variable is a trait or characteristic that we wish to measure; in the preceding example, the variable is the number of arrests per police officer. A class is one of the grouped categories of the variable. The first class, for example, is from 1 to 5 arrests. Classes have class boundaries (the lowest and highest values that fall within the class) and class midpoints (the point halfway between the upper and lower class boundaries). The class midpoint of the third class, for example, is 13; it can easily be found by adding the lower class boundary (11) and the up-per class boundary (15) and dividing by half (2) to identify the midpoint. The class interval is the difference or distance between the upper limit of one class and the upper limit of the next higher class.
eBook - PDFExperimental Design and Statistics for Psychology
A First Course
- Fabio Sani, John Todman(Authors)
- 2008(Publication Date)
- Wiley-Blackwell(Publisher)
DESCRIBING DATA 42 7 is by far the most frequent score, while in the control condition scores tend to cluster around two central values, that is 5, which is obtained by five participants, and 6, which is obtained by six participants. In order to obtain a more vivid impression of the nature of the data produced by participants in an experiment, it is possible to display Frequency Distributions in (a) Experimental condition (positive mood) Scores on logical reasoning problems –1 0 1 2 3 4 5 6 7 8 9 10 11 Scores on logical reasoning problems –1 0 1 2 3 4 5 6 7 8 9 10 11 Frequency of scores 0 1 2 3 4 5 6 7 8 9 (b) Control condition (neutral mood) Frequency of scores 0 1 2 3 4 5 6 7 8 9 10 Figure 4.1 Histograms showing data in the two conditions of our experiment: (a) experimental condition (positive mood); (b) control condition (neutral mood) DESCRIBING DATA 43 graphical ways. There are many different techniques that can be used to display fre-quency distributions pictorially. These include techniques such as box and whisker plots, and stem and leaf diagrams, but in this book we will focus on the two most commonly used techniques, that is, the histogram and the frequency polygon . The histogram The histogram is based on a set of columns (i.e., vertical boxes) that lie on a hori-zontal axis. Each single column represents a specific score that occurred at least once in the data. The height of a column corresponds to a value on a vertical axis indicating the frequency with which the score represented by the column occurred. The more frequent a score (i.e., the more often a score occurred) the higher the column. The histograms shown in Figure 4.1 display data obtained in the two conditions of our experiment. If you compare the two histograms, you can spot at a glance the different distribution of scores in the two conditions.
- Robert Pagano(Author)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
The Histogram The histogram is used to represent Frequency Distributions composed of interval or ratio data. It resembles the bar graph, but with the histogram, a bar is drawn for each class interval. The class intervals are plotted on the horizontal axis such that each class bar begins and terminates at the real limits of the interval. The height of the bar corresponds to the frequency of the class interval. Since the intervals are continuous, the vertical bars must touch each other rather than be spaced apart as is done with the bar graph. Figure 3.4 shows the statistics exam scores (Table 3.4, p. 52) displayed as a histogram. Note that it is customary to plot the midpoint of each class interval on the abscissa. The grouped scores have been presented again in the figure for your convenience. 600 500 400 300 200 100 0 Number of students Psychology Communications Undergraduate major Biological Sciences English Chemistry Philosophy figure 3.3 Bar graph: Students enrolled in various undergraduate majors in a college of arts and sciences. Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 64 C H A P T E R 3 Frequency Distributions The Frequency Polygon The frequency polygon is also used to represent interval or ratio data. The horizontal axis is identical to that of the histogram. However, for this type of graph, instead of using bars, a point is plotted over the midpoint of each interval at a height corresponding to the frequency of the interval.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
