Section 3: Examining Center, Spread, and Shape with Box Plots Q32. So far with my examination of the data, most of the data seems to be skewed. Expenditure per student and revenue per student are both skewed to the right with District of Columbia having the highest quantity. Average teacher salary is also skewed to the right. The two attributes most related to population, number of teachers and number of high school graduates, are both skewed to the right with Texas having the highest quantity. The only attribute that is not skewed to the right is students per teacher which is skewed to the left. Q33. The median of the expenditure per student data is $7168. The overall range of the data is $7341. The data is clustered in the $6000-$7500 range. The data is skewed to the right. The median of the average teacher salary data is $40476. The overall range of the data is $21948. The data is clustered in the $37000-$42000 range. The data is skewed to the right.
The median of the total number of teachers data is 42920. The overall range of the data is 283805. The data is clustered in the 0-60000 range. The data is skewed to the right. The median of the number of high school graduates data is 37385. The overall range of the data is241929. The data is clustered in the 20000-80000 range. The data is skewed to the right.
The median of the revenue per student data is $8208. The overall range of the data is $5972. The data is clustered in the $6500-$8500 range. The data is skewed to the right. The median of the students per teacher data is 15.2. The overall range of the data is 6. The data is clustered in the 14-16.5 range. The data is skewed to the left. Q34. It is easier to understand a box plot if you realize that every quartile has the same amount of data in it, even though they are various sizes. Having the dots of data displayed along with the box plot makes it easier for students to make this connection. Visually seeing the data reinforces this idea. It is easier to describe the spread and shape of data when you see the points of data. Most students can easily see the shape of data in a dot plot. Relating this to the box plot they can interpret how the box plot can show the shape of the data as well. Q35. The lower quartile of average teacher salary is $38461. The upper quartile is $43655 and the inner quartile range is $5194. The total range of this data is $21948. The big difference in the range and the inner quartile range shows that although the range is big the inner 50% of data is relatively close in amounts. This difference shows that there may be some outliers that are affecting the data.
Q36. I would use the Tukey method for my students. I feel that this will be the easiest for students to understand. I think it is important for students know how to find the quartiles no matter what technology they are using, and the Tukey method would work everytime. It also will work no matter what the data set looks like. Whether it is even or odd and if there are multiple pieces of data equal to the median. I would show students the other methods and show that you may get different answers using the different methods. I will tell them this is okay, but for consistency in this classroom we will all use the same method. Q37. Washington DC is considered an outlier in this data set. The inner quartile range of the data is $5194. 1.5($5194) = $7791. Since the upper quartile is $43655, the outliers will be values above $51446. The average salary in Washington DC is $57009, so it is an outlier. Q38. Original: Outliers Shown: The only thing that change from the original box plot to the box plot where the outliers are shown is the range and the value of the maximum.
Q39. I think that removing the outlier from the data set will drastically affect the range and mean; however, I don t think it will affect the median or the appearance of the box plot much except for the value of the maximum. Q40. Original: Modified: The median of the data did not change. The range changed from $21948 to $15200. The lower quartile changed $38461 to $38393. The upper quartile changed from $43655 to $43433 and the inner quartile range changed from $5194 to $5040. Q41. I would use the modified box plot to estimate the average teacher salary. It paints a more realistic picture of all the salaries in the South region. The outlier of Washington DC threw the data off and made it more skewed. The outlier didn t fit in with the rest of the data. Q42. I would have them use Tinkerplots to construct a box plot first. I think that the way students will be able to see the individual data plots along with the box plot will really help them grasp what
a box plot shows and represents. Also, using the technology is a great way to show the affect of outliers on box plots. Q43. Tinkerplots will really show how data is distributed in a box plot. Being able to view the data plots and box plot at the same time will make this concept clear, and the connection will be the student s own discovery. Seeing box plots on Tinkerplots will help students understand shape, centers, and ranges of different data sets and how a box plot represents all the measures.