Compared to the average, median, and mode of 6th graders’ heights, I am just below middle height. The average is 60.9577465 inches, which can be rounded to 61, being less than a tenth away. The median is exactly 61 inches; and the mode is also 61 inches. Calculating multiple measures of center is helpful in this case because we have so much data, and each measure of center shows a different part of the middle height. All measures of center are just around 61, which proves that this is the ultimate ‘middle’ height. The mean shows us what exactly each student’s height should even out to. The median shows us what height is right in the middle. The mode shows us what is the most popular height. Another reason why it is important to find multiple measures of center is to check the others. For example, if the median was 52 inches, but the average was 65 inches, you would consider a calculation error, or some major outliers.
Another thing I want to bring up is the range. The range is 20 inches; the greatest height being 72 inches (6 feet exactly) and the minimum height being 52. This is quite a surprising range, because it tells us that there is a sixth grader who is 20 inches (1”8) taller than another sixth grader. To put this in perspective, that is almost 2 heads taller. When you have such a large range, having multiple measures of center can be helpful.
When I first looked at this data, I saw a lot of clusters, which made me think there was low variability. But, when you have 142 students, having clusters of at least 8 students does not necessarily show much variability. The range of 20 has made me decide that the sixth grade Math 6+ students’ heights have a higher variability than lower. There is some low variability to consider, because the data starts like this: 52, 52, 52, 53, 54, 55, 56, 56, 56, 56… In this case, there aren’t many outliers. You can think of 52 as an outlier, but if you were to visualize this on a line plot, you would see that they are still all in one line. However, there are not clusters here either. Here is how the data ends: … 67, 67, 67, 68, 68, 69, 70, 72, 72. I wouldn’t call 72 an outlier, but again, if this were on a line plot there would be more of a line than a tall bunch. This points to high variability. But once again, the way the mean, median, and mode match up point to low variability. Quartile 1 is 58, which isn’t very close to how the data starts off. Quartile 3 is 63, which isn’t that close to the end either. So altogether, I’m going to have to say that there is low variability, even though the range is 20 inches.
To compare my height to all of this: my height is 58 inches, which is about 3 inches shorter than the middle height.
I like how you thoroughly explained how you got your answer and how you provided all the answers to the questions and then told us how you got your answer. One thing I wish you could've done is to maybe breakdown your explanation into smaller paragraphs because having all of that in one big clunk is intimidating.
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