Statistics

Statistics

• Histograms: A common method to graphically represent the frequencies data set. A histogram can be used for a larger data set. For example, if you have a large population and are gathering statistical exam scores from numerous area colleges, you may have 100 students out of 500 who receive a 94 on an exam. That is a large data set and it is not practical to generate a stem- and-leaf plot. Histograms are usually generated using graphing or statistical software. You can also generate them by hand!

Let us take a look at a histogram:

This is the typical structure of a histogram. What type of information can we obtain from a histogram? Although there are not any actual data or numerical values assigned, we can see that there are several parts to the histogram. • The purple box seems to be the highest. This represents the highest frequency for the data set. Therefore, if we were to look at a data set, the majority of the values would fall within the region of the purple box. • Now looking to the right and left of our highest frequency, we can see that the histogram is divided into two sides. The green and red boxes are to the left of our highest frequencies. These represent higher values than our frequency. If that is confusing, think of it this way: we will say the data represents the amount of time it takes students to complete an exam. Most of the students take 65 minutes to complete the exam (purple box), the red and green boxes represent the number of students who take less than 65 minutes to complete the exam. We will say red represents students who can complete the exam in 55 minutes and green represents students who can complete the exam in 45 minutes. • We also have data to the right of our highest frequency, the orange and blue boxes. In our example, these boxes would represent students who took longer than 65 minutes to complete the exam. Let’s say the orange box represents students who took 75 minutes while the blue box represents students who took 80 minutes to complete the exam. How can we interpret this data? We can say that the majority of the students can complete the exam in 65 minutes while a small portion of the student population can complete the exam in 45 minutes and 80 minutes. This information can give us an upper and lower range. 45minutes would be the fastest completion time, whereas 80 minutes would be the maximum upper time limit for the exam.

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