Frequency Polygons
Frequency polygons are graphical representations of frequency distributions. They are created by plotting points at the midpoints of the intervals and then connecting these points with straight lines. The resulting polygon provides a visual representation of the distribution of a set of data.
8 Key excerpts on "Frequency Polygons"
eBook - ePub- Debbie L. Hahs-Vaughn, Richard Lomax(Authors)
- 2020(Publication Date)
- Routledge(Publisher)
...A polygon is a many-sided figure. The frequency polygon is set up in a fashion similar to the histogram. However, rather than plotting a bar for each interval, points are plotted for each interval and then connected together as shown in Figure 2.3 (generated in SPSS using the default options). The X and Y axes are the same as with the histogram. A point is plotted at the intersection (or coordinates) of the midpoint of each interval along the X axis and the frequency for that interval along the Y axis. Thus, for the 15 interval, a point is plotted at the midpoint of the interval 15.0 and for three frequencies. Once the points are plotted for each interval, we “connect the dots.” FIGURE 2.3 Frequency polygon (line graph) of statistics quiz data. One could also plot relative frequencies on the Y axis to reflect the percentage of students in the sample whose scores fell into a particular interval. This is known as the relative frequency polygon. As with the histogram, all we have to change is the scale of the Y axis. The position of the polygon would remain the same. For this particular dataset, each frequency corresponds to a relative frequency of.04. Note also that because the histogram and frequency polygon/line graph each contain the exact same information, Figures 2.2 and 2.3 can be superimposed on one another. If you did this, you would see that the points of the frequency polygon are plotted at the top of each bar of the histogram. There is no advantage of the histogram or frequency polygon over the other; however, the histogram is used more frequently, perhaps because it is a bit easier to visually interpret. 2.2.4 Cumulative Frequency Polygon Cumulative frequencies of data that have at least some rank order (i.e., ordinal, interval, or ratio), can be displayed as a cumulative frequency polygon (sometimes referred to as the ogive curve)...
eBook - ePub- Derek L. Waller(Author)
- 2016(Publication Date)
- Routledge(Publisher)
...What they needed was a quick, clear, neat, and precise visual presentation of the hotel’s performance. Anthony pondered over the most appropriate presentation: an absolute frequency histogram; a relative frequency histogram; a polygon; an ogive; a stem-and-leaf display; a box and whisker plot; a line graph … ? The purpose of this Chapter 2 is to demonstrate some ways to visually present data so that the correct message gets transmitted. Chapter subjects ✓ Frequency distributions • Frequency distribution table • Absolute frequency histogram • Relative frequency histogram • Frequency Polygons • Ogives • Stem-and-leaf display ✓ Visuals of quartiles and percentiles • Box and whisker plot • The percentile histogram ✓ Line graphs • Candid presentations • Geometric mean as a line graph ✓ Visuals of categorical data • Pie chart • Categorical histogram • Bar chart • Contingency tables • Stacked histograms • Pareto diagram • Spider web diagram • Gap. analysis • Pictograms Using Microsoft Excel’s graphic capabilities, data can be transposed into visual displays that make interpretation and subsequent decision making easier. Most of us, even with the best education, cannot quickly and meaningfully interpret data such as presented in the Icebreaker. However, presented as a graph, histogram, or bar chart information can more easily be understood. All media publications: The Economist; The New York Times, Wall Street Journal; Time; Fortune and others either in a print version or on the Web use visual displays. They are relatively easy to understand. Frequency distributions Frequency distributions are groupings of data values into class limits to see if a pattern exists. The first step is to develop the group in a table and then from this plot the various visual aids. Frequency distribution table A frequency distribution table groups dataset values into unique categories according to how often, i.e. the frequency, that grouped data appear in a given category...
eBook - ePubStatistics
The Essentials for Research
- Henry E. Klugh(Author)
- 2013(Publication Date)
- Psychology Press(Publisher)
...These are also plotted from the data of Table 2.2. The histogram consists of a series of adjacent bars whose heights represent the number of subjects obtaining a score and whose location on the abscissa represents the value of the score. Notice that the vertical lines marking off the bars do not originate from the center of the score interval but from its edges. The edges of the individual bars mark the theoretical limits of the score intervals along the abscissa. Figure 2.4 Histogram of the examination scores tallied in Table 2.2. Figure 2.4a A histogram of the examination scores tallied in Table 2.2. Sometimes Frequency Polygons, or histograms of two different distributions, will both be plotted on the same set of coordinates. If the differences between the distributions are subtle, this procedure may highlight them. Whether one uses a frequency polygon or a histogram to represent data is largely a matter of personal preference. 2.7 Bar Charts Bar charts are the preferred graphs when data are discrete, that is, when they result from the process of counting. This convention is somewhat fluid in psychology, where ordinal scales are concerned, but it should be followed without exception for nominally scaled data, that is, for nonorderable countables. The bar chart is very much like the histogram except that spaces are left between the bars in the bar chart. Bar charts sometimes use the vertical axis to represent categories and the horizontal axis to represent frequency of occurrence. Study the bar chart in Figure 2.5 where we have graphed the enrollment in introductory courses for science departmennts at a typical college. Figure 2.5 A bar chart of enrollment in introductory science courses. 2.8 Grouped Frequency Distributions We now consider a more complex kind of frequency distribution called a grouped frequency distribution, but first we call your attention to the approximate nature of all continuous measurements...
eBook - ePub- Perumal Mariappan(Author)
- 2019(Publication Date)
- Chapman and Hall/CRC(Publisher)
...It consists of bars of the same width, each referring to class, and their heights referring to the class frequencies. Mark the midpoint of each bar on the top and move the midpoints of the preceding and succeeding classes of the initial class and the last class, respectively. Link all the midpoints using a straight line, and then the resultant graph is said to be a ‘frequency polygon’. Link all the midpoints using smooth curve (free-bend), and then the resulting graph is said to be a ‘frequency curve’. To draw the histogram, normally we take the class limits of the variable along the x -axis, and the frequencies of the class interval on the y -axis. NOTE 1 : If the class intervals are uniform in length and are not continuous, then first it must be converted into a continuous type of interval. NOTE 2 : If the class intervals do not having equal width, then the frequencies must be adjusted based on the width of the class interval. Example : Monthly sales (in lakhs of $) 10–20 20–30 30–40 40–50 Number of companies 3 4 2 1 Obviously, the lengths are uniform, and the intervals are continuous. Histogram (Figure 3.6) Step 1: Take the monthly sales along the x -axis and the number of companies along the y -axis. FIGURE 3.6 Histogram. Step 2: On each class interval, erect a rectangle (of uniform length) with the height equal to the frequency of that class. If we proceed like this, then we get a series of rectangles. 3.12.2.4 Frequency Polygon Select the midpoints of the intervals, including the preceding and succeeding class intervals. Link all those midpoints using a straight line. The resulting graph is the required frequency polygon (Figure 3.7). FIGURE 3.7 Frequency polygon. 3.12.2.5 Frequency Curve Select the midpoints of the intervals, including the preceding and succeeding class intervals. Link all those midpoints using free hand...
eBook - ePub- Jim Fowler, Lou Cohen, Philip Jarvis(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
...(See also the dot plot in Section 5.3.) 4.3 Bar graph Portraying information by means of a bar graph is particularly useful when dealing with data gathered from discrete variables that are measured on a nominal scale. A bar graph uses lines (i.e. bars) to represent discrete categories of data, the length of the line being proportional to the frequencies within that category. Suppose 31 nest boxes are placed in a wood, and 15 become occupied by blue tits, 10 by great tits, 4 by tree sparrows and 2 by nuthatches. A frequency table may be constructed: f blue tit 15 great tit 10 tree sparrow 4 nuthatch 2 — n = 31 Using these data, a bar graph may be constructed, as shown in Fig. 4.2. Fig. 4.2 Bar graph showing nest box occupancy. Fig. 4.3 Frequency distribution of orchid counts. In its final form, the horizontal dashed lines are omitted; they are included here to show that the height of the bar corresponds to the respective frequency. When observations are counts of things the bar graph is a useful way to present a frequency distribution. Illustrators often replace each bar with a vertical rectangle, or block, whose adjacent sides are touching. The frequency distribution of orchid counts shown as a dot diagram in Fig. 4.1 is shown as a bar graph in Fig. 4.3, where the height of each block is still proportional to the frequency in each category because the width of each block is equal. When presented in this form the diagram is usually referred to as a histogram. Histograms are especially useful for presenting frequency distributions of obervations measured on continuous variables, as we show in Section 4.4. 4.4 Histogram The histogram is especially useful for presenting distributions of observations of continuous variables. In a histogram the area of each block is proportional to the frequency...
eBook - ePub- Hugh Coolican(Author)
- 2018(Publication Date)
- Routledge(Publisher)
...Hence, 14.5 is the mid-point of the category 9.5 to 19.5 and these are the extremes of the interval, as explained on p. 370. Features of the histogram Columns are equal width per equal category interval. Column areas are proportional to the frequency they represent and they sum to the total area. The entire area of the histogram is considered as one unit. Columns can only represent frequencies or percentage of total frequency. No space between columns (they are not separated bars as would appear in a regular bar chart). All categories are represented even if empty. Frequency polygon If we redraw our histogram of search times (Figure 14.8) with only a dot at the centre of the top of each column we would get what is known as a frequency polygon when we joined up the dots, as in Figure 14.9. Key Term Frequency polygon Histogram showing only the peaks of class intervals. Figure 14.9 Frequency polygon of search times in Table 15.4 Exploratory data analysis Within the last few decades the emphasis on good, informative display of data has increased, largely due to the work of Tukey (1977), who introduced the term exploratory data analysis. Tukey argued that researchers had tended to rush towards testing their data for significant differences and the like, whereas they should try to spend more time and effort than previously in exploring the patterns within the data gathered. He introduced a number of techniques, and we shall cover two of the most common graphical ones here...
eBook - ePub- Richard Startup, Elwyn T. Whittaker(Authors)
- 2021(Publication Date)
- Routledge(Publisher)
...It is very easy to see where the two districts differ most in terms of the distribution of household size. Discrete data can very often be directly displayed in the form of a frequency table, but there are times when this is not appropriate. For example, if we consider the variable of school size as indicated by pupil numbers, the individual values that this variable can take will be over a considerable range, so that a frequency table would not summarise them at all well. In such cases, sets of values are grouped together in the form of (say) schools with numbers of pupils from 200 to 299, from 300 to 399, and so on. We would then have a grouped frequency table, as in Table 2.4. Although such a table is informative, it possesses one major drawback compared with an ordinary frequency table. The sizes of the individual schools have been irretrievably lost. This feature will pose problems when, later in this chapter, we come to analyse tables of this kind. Figure 2.3 Relative frequency bar chart. To present our grouped frequency distribution graphically, use is made of a histogram (Figure 2.4). In a case like this where all the group intervals are of equal length, we proceed to construct the histogram by representing the measurements or observations constituting the set of data (in this case pupil numbers) on a horizontal scale and the group frequencies on the vertical scale. The graph is then formed by drawing rectangles, the bases of which are supplied by the group intervals and the heights of which are given by the corresponding group frequencies. It should be noted that for ease of presentation the rectangles of Figure 2.4 have been made to meet at the lower limits of the group intervals, i.e. 300, 400, etc., even though the group upper limits, i.e. 299, 399, etc., in fact differ from the adjacent lower limits (precisely because of the underlying discrete nature of the data)...
eBook - ePub- Todd L. VanPool, Robert D. Leonard(Authors)
- 2011(Publication Date)
- Wiley-Blackwell(Publisher)
...That would be a mistake. Each statistical method is developed for specific situations and requires its own assumptions about the characteristics of the data. While the specific assumptions associated with each statistical method will be discussed in future chapters, it is important to understand that the patterns in the data themselves, in conjunction with the questions we ask, determine which statistical procedures are useful. Statistics are like a fine piece of clothing that must be tailor fitted for an individual. How can a suit or dress be altered if you don’t know the shape of the individual who will wear it? Therefore, the best place to start any statistical analysis is with a simple visual description. Frequency Distributions A good starting point for visually representing archaeological data sets measured at the ratio or interval scales of measurement is a frequency distribution. Figure 3.1 is a frequency distribution of the data presented in Table 3.1. The continuous variable of feature depth has been divided into 22 classes (represented in the column with the heading “Y”) with a class interval of 1 cm. Figure 3.1 Frequency distribution of Carrier Mills feature depths (cm) In Figure 3.1, Y represents the variable “feature depth”. Scanning down the column, we see that the values range from 3 to 24 cm. Each of these possible values is a class. These classes represent the possible values within which the variates that comprise our data vary. The values in the column titled Implied limit represent the resolutions of our measurements. For example, a variate with a value of 3 cm has a true depth that is between 2.5 and 3.5 cm. The Tally marks represent the number of times each value was observed and noted in Table 3.1. For example, the value 3 was observed two times...
