STA111 Lecture Note 3 - Descriptive Statistics PDF

STA111: Descriptive Statistics Topic: Presentation of Data: Chart and Graph. - Graphical Representation of Data By Dr. S.A. Aderoju Data presentation is a fundamental aspect of statistical analysis and serves...

STA111: Descriptive Statistics Topic: Presentation of Data: Chart and Graph. - Graphical Representation of Data By Dr. S.A. Aderoju Data presentation is a fundamental aspect of statistical analysis and serves as a bridge between raw data and meaningful interpretation. Effective presentation transforms complex datasets into easily understandable formats, enabling clear communication of insights and trends. In this lecture, titled "Presentation of Data: Chart and Graph", we will explore the principles, techniques, and tools for presenting data visually. Graphs and charts play a pivotal role in summarizing information in a manner that is both engaging and intuitive. They help to identify patterns, relationships, and outliers, which may not be immediately evident from numerical tables or textual descriptions. From simple bar charts and line graphs to more advanced techniques like histograms and scatter plots, graphical tools empower researchers, policymakers, and decision-makers to draw informed conclusions with ease. This lecture note is designed to: 1. Provide an overview of the key types of graphs and charts used in data representation. 2. Highlight the importance of selecting the appropriate graphical method for different types of data. 3. Demonstrate the step-by-step process of creating accurate and effective graphical representations. 4. Emphasize the role of clarity, accuracy, and simplicity in graphical communication. We consider some cases: 1) BAR CHARTS (GRAPH) Simple bar chart: A bar chart represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data. The procedure for drawing a bar graph is the following: ✓ Each value is represented with a bar (rectangle) and its height to its value. ✓ The width of all rectangles is the same (that is, equal). ✓ The bars are separated by intervals (or gaps) of equal size Example 1: The table below gives the volume of cocoa in metric tons (thousands) exported by Nigeria between 1960 and 1965. Year Metric tons 1960 73.6 1961 67.4 1962 66.8 1963 64.8 1964 80.2 1965 85.4 Figure 1: Simple bar chart Example 2: The value below shows the average money spent by third-year college students. Draw a bar graph for the data. Electronics ₦15,000, Room decoration ₦10,000, Clothing ₦13,000, Shoes ₦7,000. Figure 2: Simple bar chart Multiple bar chart: We can also construct Multiple Bar Chart which is mostly used for comparative purposes. We shall use this technique to compare the purchase of palm kernels in Kwara State from Okene and Oyun local government areas between 1971/1972 and 1973/1974 Year 1971/1972 1972/1973 1973/1974 Okene 33 19 6 Oyun 84 26 44 Total 117 45 50 2|Page  Figure 3: Multiple bar chart Component bar chart: This is a simple bar chart divided into sections such that each division (height) corresponds in magnitude to the value it represents. For example, a component bar chart for the data employed for the multiple bar chart in the previous section can be constructed as follows: i) Draw simple bars of the totals. ii) Divide each simple bar into components by just marking off respective values. Example: Component bar chart for the palm kernel data is as shown below. Figure 4: Component bar chart 2) PIE CHART The pie chart is mostly suitable for categorical variables and represents our variables or attributes in the form of circles. A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution. The procedures for constructing a pie chart are as follows; i) Find the number of degrees for each class, using the formula 𝑓 𝐷𝑒𝑔𝑟𝑒𝑒 = × 3600 𝑛 3|Page  ii) Find the percentages for each class. iii) Using a protractor, graph each section and write its name and corresponding percentage. Example: Construct a pie graph showing the blood types of STA201 students at FST Department, KWASU. The data is as shown below: Blood types Frequency A 5 B 7 O 9 AB 4 Solution Blood types Frequency No of degrees Percentage (%) A 5 5 × 3600 = 72° 20 25 B 7 7 28 × 3600 = 25 100.8° O 9 9 36 × 3600 = 25 129.6° AB 4 4 16 × 3600 = 25 57.6° Figure 5: The pie chart 3) 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. A histogram consists of a set of rectangles whose: i) bases are on the horizontal axis (X-axis) with lengths equal to the size of the class intervals. ii) areas are proportional to the class frequencies. Example: construct a histogram for the frequency distribution below. 4|Page  Solution Figure 6: The histogram 4) 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. The frequency polygon plots the frequency of each class against their respective midpoints and joining the points. Example: Using the frequency distribution given in the Example under histogram, construct a frequency polygon. 5|Page  Figure 7: The Frequency Polygon 5) CUMULATIVE FREQUENCY CHART (OGIVE) The cumulative frequency chart or ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution. The graph is plotted by plotting the cumulative frequency against the upper boundary of each class. Example: Construct an ogive for the frequency distribution described in Example 4. Figure 8: Ogive 6|Page 6) STEM and LEAVE PLOT The stem and leaf plot is a method of organizing data and is a combination of sorting and graphing. It has the advantage over a grouped frequency distribution of retaining the actual data while showing them in graphical form. A stem and leaf plot is a data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes. The steps are as follows; i) Arrange the data in order. ii) Separate the data according to the first digit. iii) A display can be made by using the leading digit as the stem and the trailing digit as the leaf. Example; At an outpatient testing center, the number of cardiograms performed each day for 20 days is shown. Construct a stem and leaf plot for the data. Solution i. Arrange the data in order ii. Separate the data according to the first digit iii. Then plot Key: 2|3 = 23 7|Page The stem and leaf plot for the data is constructed in R software with the following statements and the graph is presented as follows: (R software can be downloaded freely from https://cran.r-project.org/bin/windows/base/) Rcode: >x=c(02,13,14,20,23,25,31,32,32,32,32,3 3,36,43,44,44,45,51,52,57) > stem(x, scale = 2) 0 | 2 1 | 34 2 | 035 3 | 1222236 4 | 3445 5 | 127 Example 2 (stem and leaf plot): When the data values are in the hundreds, such as 325, the stem is 32 and the leaf is 5. For example, the stem and leaf plot for the data values 325, 327, 330, 332, 335, 341, 345, and 347 looks like this. Key: 23|4 = 234 8|Page