In this video we'll take a look at how to construct a frequency distribution
table. Frequency distribution tables are used for quickly summarizing or
tabulating a number of different values. We'll take a look at how to create a
frequency distribution table next. Suppose we have the following values
with scores for 20 people on the variable X. As you see here here we'll
make a table where we'll tabulate or count the frequency of each value of X.
First let's look at the different possible values of X that we have in our
data set. So here's our values once again notice above we have the values of X of
1 2 3 4 & 5. Let's take a look at that so here I have 1 2 3 4 & 5 and then these
remaining numbers just repeat 1 through 5 right there's no other values there's
no 6 or 7 or what-have-you so we're looking at 1 2 3 4 & 5 and the values
occur multiple times. So we'll start our table with these five possible values
and we'll start with the largest value first which is the typical way of
constructing a frequency distribution table.
So with our first step we're going to begin by making a column in the table
for X and we'll start with the value of five and then we'll work our way down
through all possible values ending in an X of 1. So here we've listed all the
possible values that occur for our variable here so we have 5 4 3 2 1 just
like we saw before. Next here we'll need to make a
column for F which represents the frequency or the number of times each
value occurs. We'll count the number of times each value occurs and then we'll
list it in the table under f or frequency. So for our example notice here
that we have one two three four, four ones in total for this variable
right so we'll count the number of times each value occurs let's do another one
we have two - we have six twos these are
assuming I've done this correctly I saw four ones and six twos so we'll make
this table here remember our X column before now we have this column F as I
had indicated earlier and we list the number of times each value occurs so
remember how we have four ones notice here we have a four here under F for an
X of one so this means we have four values of one for our variable or in
other words we have a frequency of four for x=1 the score of one we have six
values as we counted for a score of two. Here we have five threes three fours and
two fives and that's really all there is to it. So in this frequency distribution
table once we have our values summarized there's some advantages here as opposed
to when the values were all listed out like this with our table we can now draw
some quick conclusions about the data that we couldn't before.
For example, which value here occurs the most often? Well for that we would look
under F or frequency and notice here the value of six is the largest in this
column so that means that the X of 2 occurred the most often in this data set
as it occurred six times. So another way to say this is the mode is equal to 2.
Now this is important here I've seen a lot of people get confused with these
two columns and I completely understand how that can happen so it's important to
remember that this corresponds to the frequency or it counts how many times a
given value occurred so sometimes when I asked for the mode what someone will do
is they'll say the mode is 6 but the mode isn't 6 here the mode is a value
of 2 as the 2 occurred six times. Okay, so it's important to keep these two
columns straight so you'll always remember that this indicates the
frequency or the count how many times a given value occurred so 2 occurred the
most often at six times. Which value occurred the second most often? We see
that's a 3 here, right? It occurred five times and then the value that
occurred the least often is what a value of 5, right, as it occurred twice. So
the X of 5 occurred two times its frequency was two. Okay so constructing
this table allowed us to quickly summarize or organize our information
for our variable which is really one of the goals of descriptive statistics. So
these tables can be quite helpful in quickly seeing patterns of data, the
modal value, and so on. Okay that's it for creating frequency distribution tables.
Thanks for watching.