A frequency distribution is a graphical display that helps us understand our
data. It tells us important things about the characteristics of our data, such as
how many scores we have in total, and how often each of those scores appear in our
data set. Frequency is a type of descriptive statistic that organizes
data into a distribution. A distribution is the general name for any organized
set of data. In this frequency table that I created, we can see that the range of
scores is from 17 down to 10. We can also see the frequency for each score. How
many 17's are in my data set? There was one. How many 16's do I have?
There were two. I can also use this frequency table to compare the relative
frequency, cumulative frequency, and the percentile for any of these scores. As I
am preparing to serve up my data, I have two initial concerns about those scores.
First, I want to know how many scores I have in total. The question of how many
scores I have will tell me how many people completed my survey, and I'm going
to use the letter n for a number of scores to describe how many scores that
I have. The letter n is also called my sample size. My second concern is how
often any particular score occurs in my data set. How many people scored a 17? How
many people answered yes? How many people said that they were female? The frequency
will be represented with the letter F. Capital N is the notation for sample
size, or how many scores or participants we have. If 32 people answered my survey,
I have an N of 32. If 100 people answered my survey, my n would be 100. As you learn
about statistics, you may notice that you will see both uppercase and lowercase n
being used to describe sample size, and the convention works
like this. If 32 people took my survey, I would represent my sample size as
capital N equals 32. If I was describing only the 20 people who answered yes to
the first item on my survey, I would write that as lowercase n equals 20. When
you are describing only a subset of your sample, use a lowercase n. When you are
describing the entire sample, use an uppercase N. "f" is the notation for
frequency, or how often a particular score occurs. Of the 32 people, who took
the survey, 20 said yes to item one. The frequency of yes for item 1 equals 20.
Therefore with some simple subtraction, I know that the frequency of those
answering no was 12. Together with the total of yes-and-no responses, I get my
total sample size of 32. You should use a lowercase f as a notation for frequency,
or how often a particular score occurs in the data set. The symbol for frequency
will always be written as lowercase f. We will never use frequency as an uppercase
f. The uppercase f is actually referring to another type of test, the f test, or
Fisher test, which we will learn about when we study ANOVA. There is a
consistent relationship between N and f, if you add up the frequency of everyone
who said yes to the first item, 20, and everyone who said no to the first item,
12, you get our total n of 32. So n is the sum of the frequencies mathematically,
that is, N equals Sigma f.