When different data values are assigned different
weights, we will be computing, what is called
- weighted mean.
One of the examples of weighted mean is your
overall grade at the end of the course that
consists of different categories that have
different weights.
The other example of weighted mean is the
GPA score.
We will look at how to compute the GPA score.
To calculated the weighted mean, multiply
the weight of each category by the value of
that category, add the products up and divide
by sum of the weights.
Let's review the following example.
A student took 5 courses.
Her final grade, along with the number of
credits for each course, were as follows:
A in 3-credit course, A in a 4-credit course,
B in a 3-credit course, C in a 3-credit course,
and F in a 1-credit course.
The grading system assigns quality points
to letter grades as follows:A=4, B=3, C=2,
D=1, and F=0.
Computer her grade-point average.
We will start with identifying what are the
weights and what are the values of each category.
The weights would be the number of credits
that she took in each class:3
credits, 4 credits, 3 credits, 3 credits,
and 1 credit.
The value of each category is 4 for A, 3 for
B, 2 for C, 1 for D, and 0 for F.
Actually, this is 4.0, 3.3, and so on.
And you will see later why I pointed your
attention to this decimal.
The weighted mean is equal to the sum of the
products of the weight times the value.
So we multiply weights (3, 4, 3 credits, 3
credits and 1 credit) times the value of each
category (the student received A in a 3-credit
class, A in a 4-credit class, B in a 3-credit
class, C in a 3-credit class, and F in a 1-credit
class).
Then we need to add them up and divide by
the sum of the weights:3
plus 4 plus 3 plus 3 plus 1.
After we do the calculations, we find that
the numerator is equal to 43, denominator
is equal to 14.
43 divided by 14 is equal to 3.0714.
GPA is rounded to 2 decimals.
3.07 is her GPA.
And I promised you to explain why I pointed
your attention that the grades have one decimal.
Remember, mean, median and midrange is rounded
to one more decimal than the original data
value.
GPA is always rounded to 2 decimals because
the value of the category is 4.0, 3.0, and
so on.
Some institutions have grades A+, A, A-, B+,
B, B-, and so on,.
Those plus and minus range slightly with this
decimal points.That's why the GPAs are always
rounded to 2 decimals.
We will now look at how to find the mean from
a frequency distribution table.
First, we need to multiply each frequency
and the class midpoint, and then add the products,
and divide by the sum of the frequencies.
We are going to calculate the mean from a
frequency distribution table that we built
before.
First, we need to find each class midpoint.
Then multiply class midpoint by the frequency.
Remember, to calculate class midpoint, we
need to add the lower limit, the upper limit
of the class, and divide it by 2.
After you multiply each frequency by the class
midpoint, add the products up.
The result of the product of the frequency
and a class midpoint added up is 8025.
Divided by the sum of the frequencies (50)
is equal to 160.5 seconds.
Remember though, the result of 160.5 seconds
is approximation because it's based on the
use of the class midpoint values instead of
the original list of the service times.
We could, if we wanted to find more precise
value of the mean, we would add all service
times and divided them by 50 (by the number
of the values in this data set).
Coming up in the next video: chapter 3.2 Measures
of Variation and using StatCrunch to find
mean, median, mode, standard deviation, variance,
and other characteristics of the data set.
I will see you soon!
