2. STATISTICS
the study of the collection, analysis, interpretation,
presentation and organization of data. It deals with
all aspects of data including the planning of data
collection in terms of the design of surveys and
experiments.
3. MEAN
Set of observations is defined as the sum of the
observations divided by the number of
observations.
In symbols, we write mean as:
Mean = Σx/n
Where Σ is read “the sum of” and n is the number of
observations.
4. MEDIAN
The middle value or item in a set of data arranged either in
ascending or descending order.
If the number of items or values in a given set of data is even,
add the two middle scores and divide the sum by 2 to get the
median.
Example
1. Determine the median for the set of scores: {15, 18, 31, 29,
34, and 21}
Solution: Arrange the elements of the set of scores in
descending order.
34, 31, 29, 21, 18, 15
The middle scores are 29 and 21. The median of the given set of
scores may calculated by
Median (Md) = 19 + 21/2= 50/2= 25
Hence, the median of six scores is 25.
5. MODE
The value or item in a given set of data that occurs
most frequently.
Example
1. Find the mode for the following data:
36, 40, 73, 65, 36, 41, 36
Solution:
By inspection the mode is 36 (Mo = 36). It appears
thrice in the set of data.
6. STANDARD DEVIATION
Suppose you're given the data set 1,2,2,4,6. Work through each of
the steps to find the standard deviation.Calculate the mean of
your data set.
The the mean of the data is (1+2+2+4+6)/5 = 15/5 = 3.
Subtract the mean from each of the data values and list the
differences.Subtract 3 from each of the values 1,2,2,4,6
1-3 = -2
2-3 = -1
2-3 = -1
4-3 = 1
6-3 = 3
Your list of differences is -2,-1,-1,1,3
Square each of the differences from the previous step and make a
list of the squares.You need to square each of the numbers -2,-
1,-1,1,3
Your list of differences is -2,-1,-1,1,3
(-2)2 = 4
(-1)2=1
(-1)2=1
12=1
32=9
7. STANDARD DEVIATION
Your list of squares is 4,1,1,1,9
Add the squares from the previous step together.You need to
add 4+1+1+1+9=16
Subtract one from the number of data values you started
with.You began this process (it may seem like awhile ago)
with five data values. One less than this is 5-1 = 4.
Divide the sum from step four by the number from step five.The
sum was 16, and the number from the previous step was 4.
You divide these two numbers 16/4 = 4.
Take the square root of the number from the previous step. This
is the standard deviation.
Your standard deviation is the square root of 4, which is 2.
8. USE OF MEAN IN ASSESSMENT
The most well-known statistic of summary is
called the mean, which is the term we use for
the arithmetic average score. When most
people use the term 'average score,' what
they're really referring to, technically, is what
we call the mean. How do we calculate the
mean? We simply add up all of the individual
results, get the total, and then divide by the
number of students in the class. In our
example, you can see how this would look on
the screen. If you add up the scores of 20 +
17 + 16 and so on through all 20 students,
you get a total score of 210. You divide 210
by 20 (the number of students), and you get
a mean of 10.5. You can see that this score,
10.5, is a pretty representative score of the
middle score for this class, so it works nicely
as a summary.
9. IMPORTANCE OF STANDARD DEVIATION IN
ASSESSMENT
So why do we care about standard deviation at all?
Well, a teacher would want to know this information
because it might change how he or she teaches the
material or how he or she constructs the test. Let's say
that there's a small standard deviation because all of the
scores clustered together right around the top, meaning
almost all of the students got an A on the test. That
would mean that the students all demonstrated mastery
of the material. Or, it could mean that the test was just
too easy! You could also get a small standard deviation
if all of the scores clumped together on the other end,
meaning most of the students failed the test. Again, this
could be because the teacher did a bad job explaining
the material or it could mean that the test is too difficult.
10. IMPORTANCE OF STANDARD DEVIATION IN
ASSESSMENT
Most teachers want to get a relatively large standard
deviation because it means that the scores on the
test varied from each other. This would indicate that
a few students did really well, a few students failed,
and a lot of the students were somewhere in the
middle. When you have a large standard deviation,
it usually means that the students got all the
different possible grades (like As, Bs, Cs, Ds, and
Fs). So, the teacher can know that he or she taught
the material correctly (because at least some of the
students got an A) and the test was neither too
difficult nor too easy.
