Dot Plot
A dot plot is a simple way to display data using dots or points along a number line. Each dot represents a single data point, and the frequency of the data values is shown by the number of dots at each position. Dot plots are useful for visualizing the distribution and clustering of data points in a set.
8 Key excerpts on "Dot Plot"
eBook - ePub- Jim Fowler, Lou Cohen, Philip Jarvis(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
...4 PRESENTING DATA 4.1 Introduction One drawback in presenting data in the form of a frequency distribution table is that the information contained there does not become immediately apparent unless the table is studied in detail. To simplify the interpretation of the information, and to pin-point patterns and trends, the data are often processed further and transformed into a visual presentation. The most common methods of presenting data are based upon graphical techniques. In this section we describe methods suitable for presenting biological data. 4.2 Dot Plot or line plot The Dot Plot is a method of presenting data which gives a rough but rapid visual appreciation of the way in which the data are distributed. It consists of a horizontal line marked out with divisions of the scale on which the variable is being measured. A dot representing each observation is placed at the appropriate point on the scale. If certain observations are repeated, the dots are simply stacked on top of each other. Figure 4.1 shows two Dot Plots, each involving 16 sampling units: (a) Lengths of 16 leaves measured to the nearest whole millimetre: observations are scattered about 63 mm. (b) Numbers of orchids in 16 randomly placed quadrats: 7 quadrats contain no orchids. Fig. 4.1 Dot Plots showing frequency distributions of (a) 16 leaf lengths; (b) numbers of orchids in 16 quadrats. Although Dot Plots are invaluable for the preliminary analysis of data, they are seldom used as the form of final presentation. (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...
eBook - ePubStatistical Data Analysis Explained
Applied Environmental Statistics with R
- Clemens Reimann, Peter Filzmoser, Robert Garrett, Rudolf Dutter(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
...This plot is typically displayed as an elongated rectangle. Each value is plotted at its correct position along the x -axis and at a position selected by chance (according to a random uniform distribution) along the y -axis (Figure 3.2, lower diagram). This simple graphic can provide important insight into structure in the data. Figure 3.2 Evolution of the one-dimensional scatterplot demonstrated using Sc as measured by instrumental neutron activation analysis (INAA) in the samples of the Kola C-horizon In Figure 3.2 (stacked and one-dimensional scatterplot) a significant feature is apparent that would be important to consider if this variable were to be used in a more formal statistical analysis. The data were reported in 0.1 mg/kg steps up to a value of 10 mg/kg and then rounded to full 1 mg/kg steps – this causes an artifical “discretisation” of all data above 10 mg/kg. 3.2 The histogram One of the most frequently used diagrams to depict a data distribution is the histogram. It is constructed in the form of side-by-side bars. Within a bar each data value is represented by an equal amount of area. The histogram permits the detection at one glance as to whether a distribution is symmetric (i.e. the same shape on either side of a line drawn through the centre of the histogram) or whether it is skewed (stretched out on one side – right or left skewed). It is also readily apparent whether the data show just one maximum (unimodal) or several humps (multimodal distribution). The parts far away from the main body of data on either side of the histograms are usually called the tails. The length of the tails can be judged. The existence or non-existence of straggling data (points that appear detached from the main body of data) at one or both extremes of the distribution is also visible at one glance...
eBook - ePubStatistics for Psychologists
An Intermediate Course
- Brian S. Everitt(Author)
- 2001(Publication Date)
- Psychology Press(Publisher)
...Furthermore, the shape of the pattern for the odd values as the band number increases is the same as the shape for the even values; each even value is shifted with respect to the preceding odd value by approximately 4%. Fig. 2.3. Pie chart for lo percentages. (Reproduced with permission from Cleveland, 1994.) Fig. 2.4. Dot Plot for 10 percentages. (Reproduced with permission from Cleveland, 1994.) Dot Plots for the crime data in Table 2.1 (see Figure 2.5) are also more informative than the pie charts in Figure 2.1, but a more exciting application of the Dot Plot is provided in Carr (1998). The diagram, shown in Figure 2.6, gives a particular contrast of brain mass and body mass for 62 species of animal. Labels and dots are grouped into small units of five to reduce the chances of matching error. In addition, the grouping encourages informative interpretation of the graph. Also note the thought-provoking title. Fig. 2.5. Dot Plots for (a) drinker and (b) abstainer crime percentages. Fig. 2.6. Dot Plot with positional linking (taken with permission from Carr, 1998). 2.3. Histograms, Stem-and-Leaf Plots, and Box Plots The data given in Table 2.2 shown the heights and ages of both couples in a sample of 100 married couples. Assessing general features of the data is difficult with the data tabulated in this way, and identifying any potentially interesting patterns is virtually impossible. A number of graphical displays of the data can help. For example, simple histograms of the heights of husbands, the heights of wives, and the difference in husband and wife height may be a good way to begin to understand the data. The three histograms are shown in Figures 2.7 and 2.8...
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 - ePubEssential Maths Skills for Exploring Social Data
A Student′s Workbook
- Rhys Jones(Author)
- 2020(Publication Date)
- SAGE Publications Ltd(Publisher)
...This is especially relevant for disciplines that investigate changes over time, such as the sciences, social sciences, psychology, history and public health. Time series data can include changes over short or long periods. This chapter will look at several case studies that examine changes in variables over time. The main types of graph used to display data are shown below, including guidance on what the respective parts of the graph are telling you. Histograms Figure 7.1 shows a typical histogram. Figure 7.1 Histogram Dot Plots, box-and-whisker plots (sometimes just called box plots) and scatter plots Figures 7.2 – 7.4 are based on the dog walking areas data in Table 3.3. Figure 7.2 Dot Plots and box-and-whisker plots Figure 7.3 Scatter plots 1 When looking at scatter plots, we need to think about four things: Trend. Is there a linear (straight-line) relationship – in other words, can you fit roughly all the dots onto a straight line? On the other hand, do the dots appear to fit a curved line? In which case we could say there appears to be a nonlinear relationship. Alternatively, if the dots do not seem to show any pattern, we could say there is no relationship. Figure 7.4 Scatter plots 2 Scatter. Are the data points constant? If you were to draw a straight line though the data points, are they close to the line? Alternatively, is there a lot of variation in data points around the line? For example, look at the scatter plot with the blue line drawn on top of the data points (Figure 7.4). If the scatter were constant in this graph, we would expect the data points to be closer to the line, and not so spread out. Strength of relationship. If the data points are close to a line we draw as closely as possible to all the data points that we place on top, then we can say there is a strong relationship between the variables on the axis...
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 - ePub- Hugh Coolican(Author)
- 2018(Publication Date)
- Routledge(Publisher)
...Chapter 14 Graphical representation of data This chapter deals with the representation of data sets in charts or graphs. In a bar chart frequencies of data in discrete categories are presented for comparison and this must be done fairly, without visual distortion. Line charts are useful for demonstrating a time series – changes over time in a measure of a person or group. Interval data points, grouped into continuous categories, can be represented graphically as a histogram or as a frequency polygon. Tukey (1977) promoted techniques of exploratory data analysis with an emphasis on thorough examination of patterns before submitting data sets to tests of statistical significance. Two methods are included here: stem and leaf diagrams, and box-plots. SPSS procedures are included for common types of chart. Graphs in general People who dislike statistics nevertheless tend to like drawing graphs. However they are also prone to putting far too many of them into a report to make it look more interesting. It’s worth stopping to think, just what is a graph or chart for? It is not to make your report look more scientific or credible. Basically it transmits useful information to your reader. It should be a way of summing up at a glance the main features of your data or some important aspect of them. If it doesn’t do that, if it isn’t easy to understand completely (without referring to the text in your report) or if it presents the absolutely obvious, then it isn’t a good or useful chart. Before you rush to produce what many students find to be the most artistic part of a psychological research report, do take note of some cautionary advice. Over-production and decoration – don’t scatter charts around your report showing every conceivable arrangement of data and in a profusion of pretty colours and patterns. You should be very parsimonious and only produce what will be helpful, not distracting, to your reader...
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)...
