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| PICTURE #1 |
A few keys to avoid deception:
POINT #1: Frequency tables are all about summarizing COUNTS or the frequency with which something occurs, BUT NOT ALL NUMBERS IN A FREQUENCY TABLE REFER TO COUNTS! **Be sure you take the time to differentiate between numbers that represent COUNTS or FREQUENCIES and other numbers.
Look at PICTURE #1 again. Which column of numbers are counts and which are not?
COUNT RECOGNITION
ONLY the column on the RIGHT represents counts. So what are the numbers in the column on the left?
The column on the left is a number of pieces that at least one person ate. The column on the right is the NUMBER OF PEOPLE that ate that many pieces. MORE ON THIS LATER. For now just let it incubate as you move on to the next point.
POINT #2: The column on the left is a list of VALUES that someone in the dataset provided. It is clearer if we use values that are not numbers. Watch:
Now there is little (to no) confusion about which column contains the counts (frequencies) and which contains the values of the responses.
Make a frequency table for the GPA data by filling in the worksheet below. Your grade will appear on the right.
If you figured that one out--A+ to you! If not, you are probably in really good company at this point. Why? Because frequency tables can be terribly tricky and deceptive as simple as they appear to be.
REMEMBER, FOCUS ON THE COUNT!
And the COUNT lives in Column B! Column A is just telling us all the values that were actual responses. And in this case, *THERE IS NO DUPLICATE VALUE* You notice this if you are focused on the count because you would have noticed that there is only 1 total COUNT of any given response!
In other words, everyone has a different GPA in this case, so there is one response for each value and each value gets its own row:
Here is the answer key. If you didn't get it, no sweat! This was a tough one--as long as you learned to focus on the COUNT, you came out with what you needed to learn!
This brings up the next point to avoid being tricked by frequency tables:
POINT#4: Interval/ratio variables are terrible candidates for frequency tables! This is especially true when they are continuous variables. (If you need a refresher on levels of measurement, click here). However, people can and commonly do make frequency tables by changing your variable. For example, what if we made this more of an ordinal variable by having just 4 categories instead of the exact GPA?
LEFT COLUMN CHECK
See how it can get tricky?The column on the left is a number of pieces that at least one person ate. The column on the right is the NUMBER OF PEOPLE that ate that many pieces. MORE ON THIS LATER. For now just let it incubate as you move on to the next point.
POINT #2: The column on the left is a list of VALUES that someone in the dataset provided. It is clearer if we use values that are not numbers. Watch:
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| Picture #2 |
Now there is little (to no) confusion about which column contains the counts (frequencies) and which contains the values of the responses.
- 4 people said "bus" is their preferred mode of transportation
- 1 said "car (driving myself)"
- 1 said "car (getting a ride)"
- 2 said "skateboard"
- 3 said "bike"
- 5 said "walk"
- and 1 said "other"
Easy to see. Now use the same eyes to look again at Picture #1:
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| Picture #1 |
How many people answered with each of the possible responses?
FIND THE COUNTS:
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| Not this count... |
Starting to see it now? If not, here is tip #3 to master frequency tables:
POINT #3: FOCUS FIRST ON THE COUNT!
You simply will NOT fail if you focus first on the counts. In the first row of Picture #1, where is the COUNT? It is the column on the right. This is all a little facetious because it is labelled "Count". Don't worry, this is your chance to master the skill of "focusing on the COUNT". Surprisingly, this column often will be labeled either as "counts" or "frequency" or just and "f". Your job, first and foremost is to find that column. It is the absolute ground zero of the frequency table. That is why it is called a frequency table.
NOW YOU TRY>
NOW YOU TRY>
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| Picture #3 |
If you figured that one out--A+ to you! If not, you are probably in really good company at this point. Why? Because frequency tables can be terribly tricky and deceptive as simple as they appear to be.
REMEMBER, FOCUS ON THE COUNT!
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| Not this count... |
And the COUNT lives in Column B! Column A is just telling us all the values that were actual responses. And in this case, *THERE IS NO DUPLICATE VALUE* You notice this if you are focused on the count because you would have noticed that there is only 1 total COUNT of any given response!
In other words, everyone has a different GPA in this case, so there is one response for each value and each value gets its own row:
Here is the answer key. If you didn't get it, no sweat! This was a tough one--as long as you learned to focus on the COUNT, you came out with what you needed to learn!
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| Picture #4 |
POINT#4: Interval/ratio variables are terrible candidates for frequency tables! This is especially true when they are continuous variables. (If you need a refresher on levels of measurement, click here). However, people can and commonly do make frequency tables by changing your variable. For example, what if we made this more of an ordinal variable by having just 4 categories instead of the exact GPA?
- 0-0.9999 (Let's call it "VERY LOW GPA")
- 1.0-1.9999 (Let's call it "LOW GPA")
- 2.0-2.9999 (Let's call it "HIGH GPA")
- 3.0-3.9999 (Let's call it "VERY HIGH GPA")
(Notice that the ".9999" endings make it so there is no overlap between categories. Otherwise even numbers would be included in both. E.g. 2.0 would be included in both "1.0-2.0" and "2.0-3.0" categories.)
Now let's look at the new table next to the old table (the colors illustrate the way we combined the categories):
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| Picture #5 |
Notice how we start to notice some trends now. For example, a lot of people have "very high" GPAs and no one has a "very low" GPA (grade inflation at work!). you may also notice that it tells a story about measures of central tendency (MEAN, MEDIAN and MODE). Let's quickly revisit those terms in a way that is so simple it almost doesn't do justice to them:
MEAN: All the numbers added up, divided by the total number of observations.
MEDIAN: The middle number when they are all sorted from smallest to largest (or the average of the two middle numbers if it there is an even number of observations).
MODE: The most common number.
You can find all three from this table! The MODE is the CATEGORY (>AHEM< THE "***!!!CATEGORY!!!***" )with the biggest COUNT. Keep your eye on the COUNT!
In this case, what is the mode in our new table with the new categories?
MEAN: All the numbers added up, divided by the total number of observations.
MEDIAN: The middle number when they are all sorted from smallest to largest (or the average of the two middle numbers if it there is an even number of observations).
MODE: The most common number.
You can find all three from this table! The MODE is the CATEGORY (>AHEM< THE "***!!!CATEGORY!!!***" )with the biggest COUNT. Keep your eye on the COUNT!
In this case, what is the mode in our new table with the new categories?
KEEP YOUR EYE ON THE COUNT! If you answered 2 or 3 or 5, you were WRONG!! Why? Because THOSE ARE ALL COUNTS! Is the median GPA at a school the COUNT of some category? If you ask me the median GPA at Frantuckanilly State University and I told you 2,342 (the COUNT of people with an average GPA) would it make an sense to you?
POINT #5: A count (frequency) is NEVER the mean, median or mode!!
Read that sentence again 1,822 times. A count (frequency) is NEVER the mean, median or mode!
The count tells us where the mode is, but it is NOT the mode. Think of someone telling you the average GPA at their university is 9,286 and you will get the point.
So, in this case, what is the mode? Hopefully, if you got the mini quiz wrong you answered 5, because 5 is the count that indicates the mode--very high.
The mode is "very high" because it was the most frequent response.
you can also find out the mean and median, but to do this, we need to expand our frequency tables. You will learn how to do that in FREQUENCY TABLES: PART II.
POINT #5: A count (frequency) is NEVER the mean, median or mode!!
Read that sentence again 1,822 times. A count (frequency) is NEVER the mean, median or mode!
The count tells us where the mode is, but it is NOT the mode. Think of someone telling you the average GPA at their university is 9,286 and you will get the point.
So, in this case, what is the mode? Hopefully, if you got the mini quiz wrong you answered 5, because 5 is the count that indicates the mode--very high.
The mode is "very high" because it was the most frequent response.
you can also find out the mean and median, but to do this, we need to expand our frequency tables. You will learn how to do that in FREQUENCY TABLES: PART II.
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