Question

Describe and give clear, practical examples (charts, graphs, lists, etc.) of the following concepts related to Statistical Inferences using a fictitious class distribution of grades: 100 students; 20 -A's; 40 - B's; 30 - C's; 9 - D's; 1 - F:  Bar Chart; Histogram; Pie Chart; 5-column Data Set; Positive Skewed Sampling Distribution; Negatively Skewed Sampling Distribution; Scatter Plot

Answer 1

Answer.

A bar graph Bar charts can also be used to represent frequencies of categorical data where Frequencies are shown on the Y- axis and the type of grade is shown on the X-axis. Typically, the Y-axis shows the number of observations in each category. Bar charts are often excellent for illustrating differences between two distributions such as grades in English and grades in Mathematics.

A histogram is a graphical method for displaying the shape of a distribution and is helpful in plotting data on a continuous scale where the frequency for each category is represented by the height of the bar with no gap between the subsequent bars. It is particularly useful when there are a large number of observations. The histogram helps to ascertain that most of the scores are in the middle of the distribution, with fewer scores in the extremes. Histograms can be based on relative frequencies instead of actual frequencies.

In a pie chart, each category is represented by a slice of the pie. The area of the slice is proportional to the percentage of responses in the category calculated as the relative frequency multiplied by 100. Pie charts are effective for displaying the relative frequencies of a small number of categories such as the proportion of people who got grade A, those who got grade B with B showing the largest slice ( 40 students that is close to 60 percent of the area and Grade F with the narrowest area under it. They are not recommended, however, when you have a large number of categories such as if we were to compare the performance of the entire school over percentiles rather than grades.

Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data and help to discern the shape of the distribution. For instance, if we plot the grades for the class, then Most of the students fall between B and C. With fewer students getting extremely low scores. It is clear that the distribution is not symmetric inasmuch as good scores (to the right) trail off more gradually than poor scores (to the left). the distribution is thus positively skewed.

A scatter plot or line graph  is a bar graph with the tops of the bars represented by points joined by lines and the rest of the bar suppressed. Line graphs are appropriate only when both the X- and Y-axes display ordered quantitative rather than qualitative variables and they are generally better at comparing changes over time such as comparing the distribution of grades in a classroom over mid-term, final term exams.