Stat 200 - WEEK 2 SUMMARIZING AND GRAPHING

WEEK 2: SUMMARIZING AND GRAPHING DATA

CHAPTER 2.1 and 2.2
In Chapter 2, we are going to look at sets of data and explore ways of analyzing that data so that conclusions can be made from that data. Now, it is possible to have a data set that has many as 100 data points or even 1000’s of data points. We need to summarize this data in a way that makes the results more obvious and understandable. One way to summarize the data is by using a frequency table.

If you look at Table 2-1 (Academy Awards) there is a lot of data. Granted it is organized (beginning with the first awards ceremony) BUT the results are not obvious at a glance.

Now look at Table 2-2. Here the results are more direct. We can immediately see that most of the award winners were between the ages of 31 and 40. This is a simple FREQUENCY table.

How many actresses were 41-50 years old when they won? 12
How many actresses were 51-60 years old when they won? 2
How many actresses were 41-60 years old when they won? 14

Now look at Table 2-3. This is the same information, but now expressed as a percentage. Relatively speaking, this table gives us an even better idea of the data. Now we know 39% of the actresses were between the ages of 31 and 40 when they received their awards. This is a RELATIVE FREQUENCY (%) table. Magazine publishers love relative frequency tables because they can present information without having to list any confusing (or maybe compromising?) data sets. By the same token, the reader has to trust that the publisher has data sets that are accurate and representative of their claims.

What % of actresses were 41-50 years old when they won? 16%
What % of actresses were 51-60 years old when they won? 3%
What % of actresses were 41-60 years old when they won? 19%

Now look at Table 2-8. COMPARATIVE RELATIVE FREQUENCY tables are even more fun to use. We can fairly readily see that young actresses are more likely to win an award but actors can expect that they will have to prove themselves for a longer period of time before winning any award. Assuming the data is correct, then we might be able to conclude that males and females are not necessarily judged by the same sets of rules by the Oscar Awards Committees. A comparative relative frequency table allows us to critically evaluate the data. Any gap in the data larger than 5% is considered significant.

What % of actresses were 41-50 years old when they won? 16%
What % of actors were 41-50 years old when they won? 39%
What is the % discrepancy between the two groups? 15%