DATA PRESENTATION Tabular and Graphical Presentation of Data JILLIAN MARIE M. CUEVAS, RMT, MSMT Course Facilitator LEARNING EXPECTED OUTCOMES ▪ Explain the purpose and importance of data ▪ ▪ ▪ ▪ ▪ 2 presentation Enumerate the essential components of a table Discuss the meaning of graphs Enumerate the advantages and disadvantages of graphical presentation of data Identify appreciate graphs to use for a given data Discuss the description and function of the different graphs Review Basic concepts 3 Pictures of Data ▪ Depict the nature or shape of the data distribution 4 METHODS OF PRESENTING DATA 5 ▪ Textual ▪ Tabular ▪ Graphical DESCRIPTIVE STATISTICS 2. Summarize data 1. Organize data ▪ Central Tendency (or Groups’ “Middle ▪ Tables Values”) • Frequency Distributions • Mean • Relative Frequency Distributions ▪ Graphs ▪• Bar Chart or Histogram ▪• Stem and Leaf Plot ▪• Frequency Polygon 6 ▪ • Median • Mode Variation (or Summary of Differences Within Groups) • Range • Interquartile Range • Variance • Standard Deviation WHAT IS A FREQUENCY DISTRIBUTION Suppose we ask a sample of 30 teenagers each to tell us how old they are. The list of their ages is shown in Table 5.1 7 FREQUENCY DISTRIBUTION It is now easy to see how often each age occurs 8 FREQUENCY DISTRIBUTION 9 ▪ A table listing all classes and their frequencies ▪ For nominal and ordinal data, a frequency distribution consists of a set of classes or categories along with the numerical counts that correspond to each one. FREQUENCY DISTRIBUTION ▪ To display discrete or continuous data in the form of a frequency distribution, break down the range of values of the observations into a series of distinct, nonoverlapping intervals. 10 RELATIVE FREQUENCY 11 ▪ The proportion of the total number of observations that appears in that interval. ▪ It is computed by dividing the number of values within an interval by the total number of values in the table, multiplied by 100% to obtain the percentage of values in the interval. ▪ Relative frequencies are useful for comparing sets of data that contain unequal numbers of observations RELATIVE FREQUENCY 12 CUMULATIVE RELATIVE FREQUENCY 13 ▪ Is the percentage of the total number of observations that have a value less than or equal to the upper limit of the interval ▪ It is calculated by summing the relative frequencies for the specified interval and all previous ones. CUMULATIVE RELATIVE FREQUENCY 14 Text Presentation ▪ ▪ ▪ Main method of conveying information as it is used to explain results and trends, and provide contextual information. Data are fundamentally presented in paragraphs or sentences. For instance, information about the incidence rates of delirium following anesthesia in 2016–2017 can be presented with the use of a few numbers: ▫ “The incidence rate of delirium following anesthesia was 11% in 2016 and 15% in 2017; no significant difference of incidence rates was found between the two years.” 15 If this information were to be presented in a graph or a table, it would occupy an unnecessarily large space on the page, without enhancing the readers' understanding of the data Table Presentation ▪ Convey information that has been converted into words or numbers in rows and columns. ▪ Tables are the most appropriate for presenting individual information, and can present both quantitative and qualitative information. ▪ Useful for summarizing and comparing quantitative 16 information of different variables and information with different units can be presented together Graph Presentation ▪ Graphs simplify complex information by using images and emphasizing data patterns or trends, and are useful for summarizing, explaining, or exploring quantitative data. 17 GRAPHICAL PRESENTATION OF DATA 18 A. BAR CHARTS ▪ Popular type of graph used to display a frequency distribution for nominal or ordinal data. ▪ In a bar chart, the various categories into which the observations fall are presented along a horizontal axis. ▪ A vertical bar is drawn above each category such that the height of the bar represents either the frequency or the relative frequency of observations within that class. 19 20 B. HISTOGRAMS ▪ A histogram depicts a frequency ▪ distribution for discrete or continuous data. It is a bar graph in which the horizontal scale represents classes and the vertical scale represents frequencies. ▪ The horizontal axis displays the true ▪ 21 limits of the various intervals. The true limits of an interval are the points that separate it from the intervals on either side. HISTOGRAM 22 23 C. PARETO CHART 24 25 D. PIE CHART ▪ Useful for comparing individual categories with the total. 26 E. FREQUENCY POLYGONS ▪ It is constructed by placing a point at the center of each ▪ ▪ 27 interval such that the height of the point is equal to the frequency or relative frequency associated with that interval. Points are also placed on the horizontal axis at the midpoints of the intervals immediately preceding and immediately following the intervals that contain observations. The points are then connected by straight lines. FREQUENCY POLYGONS 28 FREQUENCY POLYGONS Rating (Midpoint) Frequency 29 0 - 2 (1) 20 3 – 5 (4) 14 6 – 8 (7) 15 9 – 11 (10) 2 12 - 14 (13) 1 F. SCATTER PLOTS One-Way Scatter Plots ▪ Another type of graph that can be used to summarize a set of discrete or continuous observations. ▪ Uses a single horizontal axis to display the relative position of each data point in the group. 30 F. SCATTER PLOTS Box Plots ▪ Box plots are similar to one-way scatter plots in that they require a single axis; instead of plotting every observation, however, they display only a summary of the data 31 F. SCATTER PLOTS Two-Way Scatter Plots ▪ Used 32 to depict the relationship between two different continuous measurements. ▪ Each point on the graph represents a pair of values; ▪ The scale for one quantity is marked on the horizontal axis, or x-axis, and the scale for the other on the vertical axis, or y-axis. G. Line Graphs ▪ Similar to a two-way scatter plot in that it can be used ▪ ▪ ▪ ▪ ▪ 33 to illustrate the relationship between continuous quantities. Each point on the graph represents a pair of values. Adjacent points are connected by straight lines Useful for representing time-series data Useful for studying patterns and trends across data Also appropriate for representing not only time-series data, but also data measured over the progression of a continuous variable such as distance. LINE GRAPHS 34 LINE GRAPHS 35 OTHER PICTURES OF DATA Dot Plot 36 OTHER PICTURES OF DATA Stem-and Leaf Plot 37 THANKS! Any questions? You can find me at: [email protected] 38