Data Representation, Principles Of Inferential Statistics Notes

Data Representation: Meaning, Principles and Methods Meaning of data graph: Graphic representation is another way to analyze numerical data. A graph is a type of graph in which statistical data is represented in the form of lines or curves drawn across coordinated points drawn on its surface. Graphs enable us to study the cause and effect relationship between two variables. Graphs help to measure the extent of change in one variable when another variable changes by a certain amount. The graphs also enable us to study both time series and frequency distribution because they give a clear account and an accurate picture of the problem. The graphs are also easy to understand and catch the eye. General principles of graphic representation: There are some algebraic principles that apply to all types of data graphs. In a graph, there are two lines called coordinate axes. One is the vertical known as the Y axis and the other is the horizontal called the X axis. These two lines are perpendicular to each other. Where these two lines intersect each other is called "0" or the origin. On the X axis, the distances to the right have a positive value (see Fig. 7.1) and the remaining distances to the origin have a negative value. On Y-axis distances above the origin have a positive value and below the origin have a negative value. Ways to represent frequency distribution: Generally four methods are used to graphically represent the frequency distribution. These are the graph, the smooth frequency graph and the ogive or cumulative frequency graph and the graph diagram. 1. Chart: A histogram is a non-cumulative frequency graph, plotted on a natural scale in which the representative frequencies of a different class of values are represented by drawn vertical rectangles closed to each other. Measuring the central tendency, the mode can be determined easily with the help of this graph. How to draw a graph: Step 1: Representation of the class intervals of variables along the X-axis and their frequencies along the Y-axis on the normal scale. Step 2: Start X axis with minimum minimum class interval. When the minimum happens to be a mark away from the origin, it gives a recess in the X axis to indicate that the vertical axis has been moved to rest. Step 3: Now draw rectangular bars parallel to the Y-axis over each of the class classes with the class units as a rule: the areas of the rectangles must be proportional to the frequencies of the corresponding classes. Advantages of the histogram: 1. Easy to draw and simple to understand. 2. This helps us to understand the distribution easily and quickly. 3. It is more accurate than polygene. Graph limits: 1. It is not possible to plot more than one distribution on the same axes as the graph. 2. Comparison of more than one frequency distribution on the same axes is not possible. 3. It is not possible to make it smooth. Chart uses: 1. It represents data in graphic form. 2. It provides knowledge of how scores are distributed in the group. Whether the results are cumulative at the lower or higher end of the distribution or are uniformly and uniformly distributed throughout the scale. 3. Polygon frequency. The frequency polygon is a frequency graph plotted by joining the coordination points of the mean values of season periods and their corresponding frequencies. Let's discuss how to draw a frequency polygon: Step 1: Draw a horizontal line at the bottom of the graph paper called the OX axis. Mark the exact limits of the course intervals along this axis. It is better to start with ci with the lowest value. When the lowest score in the distribution is a large number, we cannot show it graphically if we start with the source. So put a break in the X axis () to indicate that the vertical axis has been moved to rest. Two additional points can be added to the two extremes. Step 2: Draw a vertical line across the extreme end of the horizontal axis known as the OY axis. Along this line mark off units to represent frequencies of term periods. The scale must be chosen in such a way that the largest frequency (length) of the polygon is approximately 75% of the width of the figure. Step 3: I plot the points at a height proportional to the frequencies directly above the point on the horizontal axis representing the midpoint of each class interval. Step 4: After plotting all the points on the graph join these points by a series of short straight lines to form a frequency polygon. To complete this figure, two additional periods should be inserted at the high end and low end of the distribution. The frequency of these intervals will be zero. Advantages of frequency polygon: 1. Easy to draw and simple to understand. 2. It is possible to draw two distributions simultaneously on the same axes. 3. A comparison between two distributions can be made through the frequency polygon. 4. It is possible to make it smooth. Frequency Polygon Limits: 1. It's less accurate. 2. Not accurate in terms of frequency space over each time period. Frequency polygon uses: 1. When comparing two or more distributions, the frequency polygon is used. 2. It represents the data in the form of graphs. 3. It provides knowledge of how scores are distributed in one or more groups. Whether the results are cumulative at the lower or higher end of the distribution or are uniformly and uniformly distributed throughout the scale. 2. Compressed polygon frequency: When the sample is very small and the frequency distribution is irregular, the polygon is jig-jag. In order to eliminate irregularities and "also get a better idea of what the image might look like if the data were more numerous, the frequency polygon may be smoothed". In this process of tuning the frequencies, we take a series of "moving" or "running" averages. To get an exact or smooth frequency, we add a class interval frequency with two adjacent intervals, just below and class intervals. Then the sum is divided by 3. When these modulated frequencies are plotted against the class intervals in the graph, we get a smooth frequency polygon. Advantages of frequency polygon: 1. Easy to draw and simple to understand. 2. It is possible to draw two distributions simultaneously on the same axes. 3. A comparison between two distributions can be made through the frequency polygon. 4. It is possible to make it smooth. Frequency Polygon Limits: 1. It's less accurate. 2. Not accurate in terms of frequency space over each time period. Frequency polygon uses: 1. When comparing two or more distributions, the frequency polygon is used. 2. It represents the data in the form of graphs. 3. It provides knowledge of how scores are distributed in one or more groups. Whether the results are cumulative at the lower or higher end of the distribution or are uniformly and uniformly distributed throughout the scale. 2. Compressed polygon frequency: When the sample is very small and the frequency distribution is irregular, the polygon is jig-jag. In order to eliminate irregularities and "also get a better idea of what the image might look like if the data were more numerous, the frequency polygon may be smoothed". In this process of tuning the frequencies, we take a series of "moving" or "running" averages. To get an exact or smooth frequency, we add a class interval frequency with two adjacent intervals, just below and class intervals. Then the sum is divided by 3. When these modulated frequencies are plotted against the class intervals in the graph, we get a smooth frequency polygon. Ogive uses: 1. Ogive is useful for determining the number of students below a certain score. 2. When mean as a measure of central tendency is required. 3. When quartiles, canons and hundreds are required. 4. By plotting the scores of two groups on the same scale we can compare both groups. 4. Pie chart: The figure below shows the distribution of primary students on their academic achievement in school. Of the total, 60% are successful, 25% are middle picks and 15% are low achievers. Building this pie chart is very simple. There are 360 degrees in the circle. Thus, 60% of 360′ or 216° is calculated as shown in the diagram; This sector represents the percentage of outstanding students. A score of 90 was calculated for the average students (25%) and 54 for the low-achieving students (15%). A pie chart is useful when one wants to depict proportions of the total in an eyecatching way. The number of degrees can be measured "by eye" or more precisely with a protractor. Uses of a pie chart: 1. A pie chart is useful when one wants to picture proportions of the total in an eye-catching manner. 2. When a number of layers are sliced, each layer is displayed as a percentage at that time, and the pie diagram is used. Principles of inferential statistics The Normal distributions The normal distribution is a symmetrical curve shape that has one vertex and depends on probability distributions. The area under the curve represents the percentages of people or cases who got certain degrees on any variable (phenomenon) we are studying. natural curve shape