Variables1, in statistics, are any characteristic that varies with the members of the population. For example, Dr. Blackbeard’s Stat 101 class had a test and the results are in and not all had an equal score. Some score higher than others, and some scored lower. Thus, the test scores are considered a variable which in this case is a whole number between 0-25. Another variable is the amount of time the students took to study for the test. In this case, the variable varies between a second, minute, hour, or maybe even a tenth of a second. So, variables can differ depending on the situation or the information which is given. Now two types of numerical variables2 are discrete and continuous. Discrete3 is like IQ scores, SAT scores, a person’s shoes size, and so on. Continuous4 is more along the lines of height, weight, and age. Sometimes in the real world the distinction between continuous and discrete variables can be a blur. Height, weight, and age are considered continuous in theory, but they always seem to be rounded off to the nearest inch, ounce, or year, at which point they become discrete. On the other hand, money, which in theory is a discrete variable (because the difference between two values can’t be less than a penny), is mostly thought as a continuous variable because in most real life situation a penny can be thought of as an insignificantly small amount of money.
Variables can also be used to describe gender, hair color, nationality, and so on. These variables are called categorical (or qualitative) variables5. Now in some situations categorical variables must be treated differently from numerical variables. They can’t be added, multiplied, or averaged up. In other ways, you can say that both categorical and discrete variables can be treated similarly, particularly when it comes down to graphical descriptions like bar graphs and pictograms. Here are two ways to make a bar graph. It can be either vertically or horizontally. But be careful when you read a bar graph; they can be very misleading.
Another useful graph is a pie chart6; it’s mostly used when the number of categories is small. In a pie chart, the “pie” represents the entire population (100%), and the “slices” represent the categories7, with the size (angle) of each slice being proportional to the relative frequency of the corresponding category. Some relative frequencies, such as 50% and 75%, are easy to draw, but how do we draw the others like 35.6% or 27% accurately? Since 100% equals 360othen 360o/100=3.6o. It follows that the frequency 32.47% is given by 32.47*3.6o=117 (round to the nearest degree if needed). The general rule for drawing a pie chart is that the slice representing x% is given by an angle of (3.6)x degrees.

Although the distinction between quantitative and qualitative is important, it is very useful to distinguish the way you want to display your data information. Let’s say the number of categories is around the dozens, both a pictogram and pie chart will be messy with the display of numbers you have. The best way to do this is by class intervals8. For example, there are three sections to the SAT: math, English, and writing. In 2007 there were 1,494,531 college-bound seniors who toke the SAT each with a score between the minimum of 200 to the maximum of 800 for the math section. Now there is around 61 different numbers between 200 and 800. The best way is to set up a chart in grouping the numbers together. By the general rule of thumb, the number of class intervals should be somewhere between 2 and 20.So the scores would be set up along thing lines of 200-249, 250-399,…700-749, 750-800.
The process of converting test score to grades requires the set up of class intervals. Using the grading scales (A=90-100%, B=80-89%, C=70-79%, D=60-69%, F=0-59%) is one standard approach to use as an absolute grading scale where the class intervals are of (almost) equal length except for F. Another approach is to use a relative grading scale. The professor fits class intervals for the grades to the performance of the class in the test; also known as “grading on the curve”. After looking at the overall class performance, Dr. Blackbeard decides to “curve” the test scores to his own class intervals in which he created. Both the class intervals and the corresponding results are in the graph show. When there are no gaps between the class intervals, using separate columns or stacks will no longer be affective. That’s when we will use a variation of a bar graph called a histogram9. Suppose we want to display last year’s graduate students’ salaries in a graph from Tasmania State University. Starting Salary of the N=3258 graduate range from a minimum of $40,350 to a maximum of amount of $74,800. Based on the amount of detail you want to show, we need to deice on the class intervals we want to use. Now the table 14-6 shows that we choose a class interval of $5,000 difference. Unlike bar graph, histograms are used for contiguous variables, there can be no gaps in between the bars, and they have to touch. Also, this forces us to make a decision in which value falls on which side: left or right. This is called the endpoint convention. The “plus” mark in the graph to the right represents how to chose the deal with the endpoint convention. A starting salary of exactly $50,000 would be listed under the 45,000+-50,000 rather than the 50,000+-55,000 because the 50,000+ is more than 50,000.

1. Variables - any characteristics that varies with the member of population. 2. Numerical Variables -a variable that represents a measurable quantity. 3. Discrete -when possible values of the numerical variable change by minimum increment. 4. Continuous -when the difference between the values of a numerical variable can be arbitrarily small. 5. Categorical Variables –variables that describes characteristics that cannot be measured numerically. (hair color, gender, nationality, and so on) 6. Pie Chart –a circular graph divided into sectors proportional to the magnitudes of the quantities represented. 7. Categories -class 8. Class Interval –one of a set of intervals of arbitrary width into which the range of a sample of measurement is partitioned. 9. Histogram -A graphical representation, similar to a bar chart in structure, that organizes a group of data points into user-specified ranges. The histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.