Both histograms and frequency tables have positives and negatives. Histograms
portray the shape of the data but you lose the individual scores. Frequency
tables maintain those individual scores, but we don't see the shape of the
distribution. But what if you want both? To get the best of both worlds, to see
both the shape of the data and keep the individual scores, use a stem-and-leaf
diagram. Histograms show the shape of the data but you lose the individual scores
Here we see a bimodal distribution, but it's difficult to tell how many 5's
there are in the data set. Frequency tables retain the individual scores so
we can see how many 5's there are, but they don't show us the shape. The table
gives us individual frequencies, but we can't imagine how they will look when
they are plotted. To see both the shape and keep the individual scores of the data,
use a stem-and-leaf diagram. But in order to understand this, we need to recall one
important thing you probably remember this from first grade math. When you were
learning about numbers, you know that every number in the world, no matter how
large, comprises some combination of the numbers 0 through 9. When we have a
single number, we might say that that number is in the "ones place".
What we mean is that we have a single-digit. If all we had were those
ten single digits, we could actually do quite a bit, maybe most of what we need
to do in real life. But we could not do complex math, or accounting, or business.
So we have rules about combining numbers. The first rule is we can add a
second digit, and if we add a second number we now have digits in the
1's place and a digit in the 10's place
Add a third number.
We have a value in the "hundreds place". A fourth number goes in the
"thousands place" and so on. So, if we consider the number "25",
it has a 2 in the tens place and a 5 in the ones place. A stem-and-leaf diagram
puts the tens column as the stem, and the leaves are the 1's column. So the first
number in this stem and leaf is 1 & 4, or 14. The row for with 3-3-4, that
contains the numbers 43, 43, 44. Go down here, we have four 65's. Zero is still a
number so 9 / 0 is 90. The highest number in our data: 98. The lowest number: 14.
We have four 70's and the most frequently occurring score is 69. In this
case, we have a lot of numbers, so we split them 0-4 and 5-9. Because we
have the same number in the tens column, to keep them straight
we use an asterisk. For instance, use 6 to represent the values between 60
and 64, but 6* represents the values between 65 and 69. The asterisk
helps show that the sixties have been divided on purpose. Finally, we want
to see the shape of the data. To do that, we could turn the stem-and-leaf diagram
on its side, and we have a histogram. We see both the shape of the data and we
keep the individual scores. You create a stem-and-leaf using the Explore command
in SPSS. Using the dataset Clickers. sav go to Analyze - Descriptive Statistics -
Explore. We're going to move participation from round 1 into the
dependent list and now click on Plots. You'll notice that stem and leaf is
already selected, so we don't actually need to do anything here. Let's just
click Continue and OK. This will create both a stem-and-leaf and the box plot
along with various other descriptive statistics.
There's our stem and leaf, and there's the box plot