Module 2

Annenberg:

QUESTION B1: Using the data above, answer this question: How many raisins are in a half-ounce box of Brand X raisins? Answer the question in whatever manner seems the most descriptive.

The first thing that I did for this question was plug the data into the chart. This let me see all of the numbers. The first thing that I noticed was that 28 was the most common number of raisins in each box. I was going to stop there since that is the mode, but out of curiosity, I wanted to know if the median would give the same number. I lined the numbers up and, again, I got 28! So I concluded that a box of raisins would have 28 raisins on average.

Problem B3

Does Problem B2's data strongly suggest that the next box will have 28 raisins? Does it prove that the next box will have 28 raisins? If so, why? If not, would there be a way to prove, statistically, that the next box must have 28 raisins? I was a little confused by this question. Initially I would say that, yes, there will be 28 raisins in the next box. The past 17  boxes all had exactly 28 raisins. It seems very likely that the next box would also contain 28. Other than showing the data supporting that claim, I'm not sure how you could prove that this is true.

Median

I actually made a mistake when I first plotted my data! I confused a line plot with a line graph so I had to go back and do it again!

Kindergarten Data:

Mode: 0

Median: 0

1st Grade Data

Mode:7

Median: 5.5

2nd Grade Data

Mode: 8

Median:8

 3rd Grade Data

Mode: 9

Median: ? (I'm not sure how to find the median when there are unknowns)

Just from glancing at the four line plots we can tell that at least one student in each grade has lost at least 1 tooth. As the grade level rises, so does the number of teeth lost. In the Kindergarten class, there were more people who had not lost any teeth than there were people who had lost teeth. In the 2nd and 3rd grade classes everyone had lost at least 2 teeth.

If only the mode for each class was given, we would know the most common number of teeth that each class had lost. If we only knew the mode, we would have no idea about the outliers. For example, the mode for 3rd grade is 9 teeth, yet there is also a student who lost 19 teeth! If I thought that most of the class had lost 9 teeth I would never consider that someone had lost as many as 19.

Only having the median would not really give you a clear picture of the data unless you also knew  the range. When you know the range you know that the class has lost anywhere from x-y many teeth. The median gives you an idea of what the average number lost was.  for 2nd grade you would know that they had lost between 2-13 teeth. On average they lost around 8. You would not know, however, that most of the class had lost 8 or more teeth. 

I Scream

The opening statement was a bit surprising. I don't really think about 4 year-olds gathering and representing data! The kindergarten lesson in the article seemed like it would be a bit ambitious for students to do independently. I think the teacher did a great job letting the students take the lead. They all seems very excited and motivated which I think makes a big impact. The point of the lesson was to let the students individually practice these graphing and data skills that they have been exposed to in a full class setting.  I like that the teacher allowed students to pick their preferred style of graph. Though the data was not the most accurate, all of the students represented their data successfully.