Now that we know what frequency is, let's create our first frequency table. The
term "simple frequency" refers to the number of times a score occurs in the
data set. To calculate simple frequency, we simply count the number of
occurrences for each score in the data. To create a frequency table, we begin by
creating columns of numbers, called an X column, where we will list all of the values
that appear in the data set in descending order. Next, we will create a
frequency column, where all of the simple frequency values are going to go. The
scores in the X column are always arranged in the descending order of
magnitude. In other words, the largest score goes on top, the smallest score
will be at the bottom. Now in biological sciences, frequency is cycles per second
and its measured in "Hertz" named after Heinrich Hertz. Now of course, to create a
simple frequency distribution, we will need some data, so let's take a poll. I'm
asking everyone in the class, how many pets do you have at home. You can count
dogs, cats, fish, birds. Add up how many of them you have. Now for the purposes of
this video, I'm going to pretend that I have surveyed 10 people and I've collected
some data points. These are the data that i'm going to put into my simple
frequency table. So here you can see my data points. I will begin by creating an
X column, and then using the data points arranged in descending order. The largest
value in my data set is a 4, so I will arrange the order descending, 4, 3, 2, 1, and
the lowest value will be 0. Now what would we do if one of these values was
missing? What if no one had three pets at home? The answer is - we would still
include the three in our X column, but it would have a frequency of zero.
In the X column, we want to include the full range of our data, including values
that are missing. We will create the f column using the frequency scores. So how
many people had four pets at home according to our survey? Only one. How
many people had three pets? Also one. Now by the way, when working by hand you will
find it beneficial to cross out the numbers as you count them. What was the
frequency for two pets? Three. How about for one pet? Two. And the frequency for zero pets was
three. So now i have created my simple frequency table. You should add these
numbers to your pet data table in your notes. Next I'm going to create another
column for the relative frequencies in the data. The relative frequency is a
number between zero and one that represents the proportion of time the
score occurs in the data set. The term "proportion" refers to a ratio or division.
Therefore, the relative frequency is going to be the frequency divided by n.
Because my n equals 10, i will divide each frequency in the X column by 10. For
the score of 4, with a frequency of 1, 1 divided by 10 is .10. That is the first value
of my relative frequency column. The score of three also has a frequency of
one, so it also has a relative frequency of .10. The frequency of 3 divided by 10 is
.30. Frequency of 2 divided by 10 is .20, and for those who have no pets at home,
those three people have a relative frequency of .30. Now here we have
an opportunity to check our work. Because relative frequency is a number between 0
and 1 that is a proportion of the whole, if we add up the relative frequency
column. It should always add up to 1. If it doesn't, we've made a mistake we
should go back, and check our math. If you have not already add these
numbers to your pets data table in your notes. Now we will add a column for
cumulative frequency. The word "cumulative" means to accumulate it refers to the
frequency of scores at or below a particular score. Let me illustrate
cumulative frequency using two graphs. In this first graph, scores are plotted with
separate lines for each year. We can see how the scores for a particular month
compared across the years. In this graph, the scores are plotted using cumulative
frequency. The cumulative frequency line always goes from the lower left to the
upper right. The steepness of the line gives an indication how much more was
being added to the line. The line will never descend because it is cumulative.
Once we have added to it, we cannot go back, if nothing more is being added, then
the line will flatline. Of course, we can only use cumulative frequency with
interval and ratio level data. We cannot accumulate categorical data because it
does not have an underlying order. To calculate the cumulative frequency will
begin with the lowest x value in our data set, so the first cumulative
frequency value will be the same as the frequency value for the smallest score
in our data. How might we use relative frequency? Perhaps we are selling tickets
to a play in four weeks. Each week, we keep track of the number of tickets that
have been sold. Hopefully, at the end, the cumulative frequency adds up to the
total number of seats available, and our show has been sold out. Or perhaps we're
plotting the number of fatalities that have occurred since the beginning of the
war. Each month we tabulate new totals, and plot them with an ever increasing
line. When the line is flat, good news. No new fatalities are being added. When the
line ascends rapidly, many more people are getting killed. Returning to our pets
data, the first cumulative frequency value
will be the same as the frequency value for the smallest score in our data. In
this case, zero has a frequency of two, so that is our first cumulative frequency
value. Remember that we are starting at the bottom of the cumulative frequency
column this time. Now we begin to accumulate frequencies. For the next
cumulative frequency, the answer will be 3, plus the next frequency score, which is
2, for those with only one pet. Three plus two equals 5, so 5 is the cumulative
frequency for the score of 1. To the five we add three, the next frequency value,
and get a total of eight. Eight plus one equals 9, 9 plus 1 equals 10, that is our
final cumulative frequency value at the top of the column. Here again we have an
opportunity to check our work, because the sum of the frequencies always equals
the sample size, the top cumulative frequency value will always equal n. Now
add these values to your notes. We are going to add one last column to our
table, and that is percentile. A percentile is the percentage of all of
the scores in the data that are at or below a certain score, so perhaps you've
taken the scholastic aptitude test and you scored at the 89th percentile, that
means eighty-nine percent of people who took that same test scored the same or
below you. Or maybe you got a checkup with your doctor and found out that your
weight is in the 23rd percentile, that means twenty-three percent of people are
thinner than you, and the remaining seventy-seven percent are heavier than
you. We will calculate the percentile by dividing the cumulative frequency by n,
then multiplying the result x 100, so let's do that. You can see here that each
cumulative frequency score was divided by 10 then multiplied by 100. Beginning at the top of
the percentile column, the cumulative frequency of 10 divided by the N of 10 equals 1, times
100 equals the percentile of 100 for the x value of four. Working down the
percentile column 9 divided by 10 equals .90, x 100 equals 90. 8 divided by 10 equals .80 times
100 equals eighty. 5 divided by 10, times 100 equals 50, 3 divided by 10 times 100 equals 30. Go ahead and complete
the table in your notes if any of these numbers are still missing. And now, it's
your turn, you have been given a set of data in the notes. See if you can create
a frequency table using that data. Be sure to include simple frequency,
relative frequency, cumulative frequency and percentile, and here's a hint - as you
are creating your first simple frequency column, you will find it helpful to cross
out the numbers as you use them. Before you move along, be sure that your
frequency column adds up to a total n of 20. Pause the video now, and when you're
done with your frequency table, I will show you the answers.
Use this table to check your work. If you made a mistake, try to figure out where
you went wrong and correct it. Making mistakes is part of learning.