Kathrin Lemoine
MBA 8011-chpt. 2 continued
- The above histogram depicting the distribution of elevator rails in diameter is an example of a symmetric histogram. That is, it has a single peak in the center and is approximately the same to the left and to the right of the peak.
- The diameter of elevator rails ranged from slightly less than 0.455 inches to slightly more than 0.545 inches. Since the majority of the data fell within a 0.1 inch range, we chose to have 11 categories, each being 0.01 inches in length.
- This histogram clearly shows that most elevator rails are between 0.495 to 0.505 inches in diameter.
- Another shape of a histogram is a positively skewed histogram (skewed to the right). In other words, there is a single peak and the values of distribution extend much farther to the right of the peak than to the left of it.
- The data ranged from less than 2.5 minutes to more than 27.5 minutes. We chose to use 12 categories and since the difference between 0 and 27.5 is 27.5 divided by the chosen 12 categories, making each category 2.5 minutes in length.
- The histogram tells us that a travel time of more than 15 minutes is very rare and that the majority of time is under 2.5 minutes.
- The histogram showing the distribution of midterm scores is negatively skewed. The tail to the left of the peak is longer than the tail to the right. Negatively skewed distributions are less common than positively skewed distributions. However, the distribution of grades in a class is often negatively skewed where the majority of the class does quite well and only a few students with low grade bring the class average down.
- Again, we chose to use 12 categories, each 5 in length. There was no need to extend the categories below 45 since only very few students made such grades.
- This histogram show that most students scored between 85-90 on their midterm exam.
- The above histogram was constructed from the combined frequency distributions of two different machines. We have ended up with a bimodal histogram, a histogram that has two distinct peaks.
- Bimodal histograms often tell us that the data come from two or more distinct populations, which we already know to be true in this example.
- It is interesting to note how each machine compares to the other as far as the length of elevator rails they produce. However, to see the distribution of each machine more accurately, it would be better to chart their distributions separately.
