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This lecture covers how to organize and summarize data using frequency distributions, histograms, bar graphs, pie graphs, scatter plots, and line graphs.
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www.hndit.com Statistics for IT Lecture 3 part-2: Organization and Summarization of Data
www.hndit.com Course Objectives • After completing this module, students should be able to • Organize data using a frequency distribution. • Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives. • Represent data using bar graphs, pie graphs, scatter plot and line graphs.
www.hndit.com What is a bar chart? • When the data are qualitative or categorical, bar graphs can be used to represent the data. A bar graph can be drawn using either horizontal or vertical bars. • A bar graph represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data • Bar charts are a type of graph that are used to display and compare the number, frequency or other measure (e.g. mean) for different discrete categories of data. • There are several variations of the standard bar chart including • horizontal bar charts, • grouped or component charts, • and stacked bar charts.
www.hndit.com What is a bar chart?.... • The chart is constructed such that the lengths of the different bars are proportional to the size of the category they represent. The x-axis represents the different categories and so has no scale. In order to emphasize the fact that the categories are discrete, a gap is left between the bars on the x-axis. The y-axis does have a scale and this indicates the units of measurement.
www.hndit.com What is a bar chart?.....
www.hndit.com Horizontal bar charts • This is a particularly effective way of presenting data when the different categories have long titles that would be difficult to include below a vertical bar, or when there are a large number of different categories and there is insufficient space to fit all the columns required for a vertical bar chart across the page.
www.hndit.com Horizontal bar charts…
www.hndit.com Worked Example • College Spending for First-Year Students • The table shows the average money spent by first-year college students. Draw a horizontal and vertical bar graph for the data.
www.hndit.com Solution
www.hndit.com Grouped bar charts • Grouped bar charts are a way of showing information about different sub-groups of the main categories. • A separate bar represents each of the sub-groups and these are usually colored or shaded differently to distinguish between them
www.hndit.com Stacked bar charts • Stacked bar chars are similar to grouped bar charts in that they are used to display information about the sub-groups that make up the different categories. • In stacked bar charts the bars representing the sub-groups are placed on top of each other to make a single column, or side by side to make a single bar. The overall height or length of the bar shows the total size of the category whilst different colors or shadings are used to indicate the relative contribution of the different sub-groups.
www.hndit.com What is a pie chart? • The purpose of the pie graph is to show the relationship of the parts to the whole by visually comparing the sizes of the sections. Percentages or proportions can be used. The variable is nominal or categorical. • A pie Chart is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.
www.hndit.com Worked Example • Super Bowl Snack Foods • This frequency distribution shows the number of pounds of each snack food eaten during the Super Bowl. Construct a pie graph for the data.
www.hndit.com Solution
www.hndit.com The Histogram • The histogram is a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.
www.hndit.com Worked Example • These data represent the record high temperatures in degrees Fahrenheit (F) for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes. • Construct a histogram to represent the data shown for the record high temperatures for each of the 50 states.
www.hndit.com Round the answer up to the nearest whole number if there is a remainder: Subtract one unit from the lower limit of the second class to get the upper limit of the first class. Then add the width to each upper limit to get all the upper limits. 105 - 1 =104 The first class is 100–104, the second class is 105–109, etc.
www.hndit.com The Frequency Polygon • Another way to represent the same data set is by using a frequency polygon. • The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points.
www.hndit.com Worked Example • Using the frequency distribution given in Example in slide 20, construct a frequency polygon.
www.hndit.com Answer • Find the midpoints of each class.
www.hndit.com The Ogive • The ogiveis a graph that represents the cumulative frequencies for the classes in a frequency distribution.
www.hndit.com Worked Example • Construct an ogive for the frequency distribution described in Example in slide 20.
www.hndit.com Answer
www.hndit.com The scatter plot • A scatter plot is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data. • The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.
www.hndit.com Line Graphs • Line Graph - A graph that shows information that is connected in some way (such as change over time). • Eg. • You are learning facts about plannets, and each day you do a short test to see how good you are. These are the results:
www.hndit.com • Thank You!
