Welcome to an example on how to use the one variable statistics tool
on the TI-84 graphing calculator. In this video we'll look at an example
where we also have a frequency table. When we run the one variable statistics on the TI-84,
we're able to get all the information about the data shown here.
Where X bar is equal to the mean or average. The sum of x is equal to the sum
of the data values.
The sum of x square is equal to the sum of the squares of data values.
Sx is the sample standard deviation.
Sigma X is the population standard deviation.
N is the equal number of data values. On the next page
minX is the minimum data value, Q1 is the first quartile,
m-e-d is the median, Q3 is the third quartile,
and maxX is the maximum data value.
It's important to note though that there are several methods for determining
the first and third quartiles, so before using these
we do want to make sure we're supposed to use the method used by the TI-84
graphing calculator.
And for my research I found that the TI-84 graphing calculator uses the formula
point two,five,
times the quantity n plus one to calculate the position of lower quartile.
And point seven, five times the quantity of n plus one,
to calculate the position of the upper quartile, or quartile three.
And the calculators return the average position between the measurements
instead of the exact position or rounding to a particular position
used in some stats software packages, if the position
is a decimal. Another way to explain how the TI-84 calculator find the quartiles,
would be to say that the lower quartile, or Q1 is the median of the lower half of the
data.
The upper quartile, or Q3 is the median of the upper half of the data.
However if the median is the data value it is not considered to be in the upper
or lower half
of the data. So looking at these two examples where we have an even number of data
values,
notice how the median here would be fourteen,
and here we'd have a median of fifteen point five. In these two examples,
the median is not a data value, and therefore Q1
is the mean of seven and nine, which is eight.
And Q3 would be the mean or average of sixteen and twenty, which is eighteen.
In this example, the median of the lower half would be nine, and so Q1 is nine,
and Q3 would be the median of the upper half, or twenty-four.
Now let's look at two examples where we have an odd number of data values.
Because we have an odd number of values, notice how the median is a data
value,
both here and here. So the TI does not consider it
in the upper or lower half. And therefore, Q1 is going to be the mean or average of
seven and nine ,which is eight. And Q3 is going to be the average of twenty and twenty-four, which
is twenty-two.
Here though, because we have an odd number of data values in the lower and
upper half,
because TI does not consider the median in the upper or lower half,
Q1 is nine, and Q3 is twenty-six.
This is important to recognize because if your quart does not use the same
technique in order to find the quartiles
you don't want to rely on eighty-four to find the quartiles for you.
And in fact, in our class we actually are not using the same method
that the TI-84 does, we use the method outlined here.
Let's go and take a look at an example
where we use the TI-84. We're asked to determine the mean,
median, sample, and population standard deviation,
and the five number summary. Normally we would not find both the sample,
and population standard deviation. If the data was the sample,
we'd use only the sample standard deviation. If the data was the entire population,
we would only use the population standard deviation.
For the first step let's enter the data. So enter the data values
in L1, and the frequency in L2.
Notice because sixty-five has a frequency of two,
there are two data values of sixty-five. Because the frequency of seventy-three is three,
there are three data values of seventy-three, and so on.
So we'll press stat, and then
enter. Because we have old data in L1, we'll go to the top of the column,
press clear, and then enter. And now we'll enter the data values. So we have sixty-five,
enter, seventy-three, enter, and so on.
And now we'll press the right arrow,
and enter the frequency. So two,
enter, three, enter, and so on.
And now we'll run the one variable statistics,
so we'll press the stat key, right arrow wants to calculate.
And the first option is one variable statistics.
So we can either press number one or enter, because one is highlighted,
so we'll press enter. Now I have a newer version of the TI-84.
I'll show the screen for the older version in just a moment. Notice here it's
asking for list.
Our data is in L1, so this is correct, press the down arrow.
The frequency list though, is in L2, so we want to enter L2 by pressing
second, number two, arrow down to calculate,
and press enter. Now before we gather the information that we need,
I do want to show the screenshot from the older version of eighty-four,
or the eighty-three. Once we have one-var statistics on the home screen,
using the older version, we need to select the list for the data values,
and the list for the frequency. So notice here, the data values was in L1 so we select L1
by pressing
second one, comma ,and then enter,
second two for L2 to indicate where the frequency is located.
And then from here, we would just press enter, which brings us to this screen.
So this tells us x bar, or the mean would be approximately eighty-two
point three, six. From this screen we also see that the sample standard deviation
would be approximately eight point five, nine. And the population standard deviation would be
approximately,
notice we rounded two decimal places, rounding up. So to two decimal places this would be
approximately eight point four, zero.
So our mean would be approximately eighty-two
point three, six. The sample standard deviation
is approximately eight point five, nine. And the population standard deviation
was approximately eight point four, zero.
Now we'll press the down arrow to go to the next page.
Notice how the median is equal to
eighty-one.
And then the five number summary is going to be
the min Q1, the median Q3,
and the max. So we have sixty-five, comma, eighty-one,
comma, eighty-one, comma eighty-eight, comma, ninety-five.
And again just remember, there are several methods to determine
Q1 and Q3. So before we use these values
it's important to make sure you're supposed to use the same method
as the TI-84. And remember for our class we are using a different method.
I hope you found this helpful.