2. MEASURES OF CENTRAL TENDENCY
In education, measures of central tendency—such as mean,
median, and mode—serve as vital tools in assessing
student performance. These statistics offer insights into the
typical trends within a set of data, enabling educators to
make informed decisions, identify patterns, and refine
teaching strategies. As fundamental components of
educational assessment, these measures contribute to a
data-driven approach, ultimately enhancing the overall
learning experience.
3. MEAN
The mean, a central measure of tendency, is extensively
used in learning assessments to provide a representative
average of student performance. Calculating the mean
enables educators to gauge the overall performance of a
group, aiding in data-driven decisions and targeted
improvements in teaching strategies.
4. MEAN
It is the most frequently used measure of central tendency
because it is subject to less error; it is rigidly defined; and
it is also easily calculated. Likewise, it lends itself to
algebraic manipulation; its standard error is less than the
median; and the sum of the deviation of the cases about
mean is zero.
5. MEAN
Illustration: Consider the results in 80-item Calculus test by
10 teacher education students who major in Mathematics.
The score are as follows: 80, 79, 78, 78, 75, 73, 70, 68,
65, 63.
ത
𝑋 =
σ 𝑋
𝑁
=
80+79+78+78+75+73+70+68+65+63
10
=
729
10
= 72.9
7. MEDIAN
In learning assessments, the median serves as a valuable
measure of central tendency, representing the middle
value in a dataset. It is particularly useful in education for
assessing student performance, offering insights into the
central point of a distribution and helping educators better
understand the overall academic landscape within a
group.
8. MEDIAN
Illustration: Find the median of the following scores: 80, 79,
78, 78, 75, 73, 70, 68, 65, 63.
෨
𝑋 =
(75+73)
2
= 74
9. MODE
In learning assessments, the mode, a key measure of
central tendency, identifies the most frequently occurring
value in a dataset. Its application in education allows
educators to pinpoint common trends in student
performance, aiding in the identification of prevalent
strengths or challenges within a group. This facilitates
targeted instructional adjustments for improved learning
outcomes.
11. ADVANTAGES AND DISADVANTAGES OF THE MEAN
Advantages Disadvantages
1. Mean is the best measure
for regular distribution
1. Mean does not supply
information about the
homogeneity of the group
2. It is most reliable 2. The more heterogeneous
the set of observations or
group, the less satisfactory is
the mean
12. ADVANTAGES AND DISADVANTAGES OF THE MEAN
Advantages Disadvantages
3. It is most stable
4. It has least probable
error
5. It is generally the most
recognized measure of
central tendency
13. ADVANTAGES AND DISADVANTAGES OF THE
MEDIAN
Advantages Disadvantages
1. Median is the best
measure of central tendency
when the distribution is
irregular or skewed.
1. Median necessitates
arranging of scores
according to size before it
can be computed
2. It may be located in an
open-end distribution or
when the data is incomplete
wherein only 80 percent of
the cases are reported
2. It has larger probable
error than the mean
14. ADVANTAGES AND DISADVANTAGES OF THE
MEDIAN
Advantages Disadvantages
3. It is preferable when the
units of measurement are
unknown and is determinable
from cumulative curves or
other graphs like the ogive or
cumulative percentage
frequency line graph
3. It does not lend itself to
algebraic treatment
4. It is erratic when the
data do not cluster at the
center of the distribution
15. ADVANTAGES AND DISADVANTAGES OF THE MODE
Advantages Disadvantages
1. Mode is always a real
value since it does not fall on
zero
1. Mode is inapplicable to
small number of cases
when the scores are not
yet repeated
2. It is easy to approximate by
observation especially if the
number of cases is small
2. It is also inapplicable
when all the scores have
the same frequency
16. ADVANTAGES AND DISADVANTAGES OF THE MODE
Advantages Disadvantages
3. It does not lend to
algebraic manipulation
3. It is inappropriate
measure for irregular
distribution
4. It does not necessitate
arranging of values for it can
be taken through inspection
17. MEAN FROM GROUPED DATA
Mean from grouped data in a form of frequency
distribution is applied when the number of cases (N) is 30
or more. There are two methods in computing the mean
from grouped data. These are: (1) midpoint method, and
(2) class-deviation method.
18. MEAN MIDPOINT METHOD
Mean from midpoint method is done by getting the product of
the midpoint and frequency. The formula is as follows:
ത
𝑋 =
σ 𝑓𝑀
𝑁
ത
𝑋 – Arithmetic mean
σ 𝑓𝑀 – summation of the product of midpoint times frequency
𝑁 – Number of cases
19. MEAN MIDPOINT METHOD
To apply the formula in previous slide, consider the steps
below:
1. Compute the midpoint of all class limits, which is given
the symbol M.
2. Multiply the midpoint by the corresponding frequency.
3. Sum the product of midpoint by frequency to get σ 𝑓𝑀.
4. Divide the sum by the number of cases (N) to get the
mean.
22. MEAN CLASS-DEVIATION METHOD
This method is known as class-deviation method because it
deals with the deviation observed values instead of raw
scores from arbitrary origin in any of the class limits. The
point of origin that is arbitrarily chosen is zero. If class
limits are arranged from highest to lowest, above zero
deviation is positive and below it is negative. If class limits
are arranged from lowest to highest, above the zero
deviation is negative and below it is positive.
23. MEAN CLASS-DEVIATION METHOD
The formula in getting mean of the class-deviation method
is as follows:
ത
𝑋 = 𝑀0 + 𝐶
σ 𝑓𝑑
𝑁
Where: ത
𝑋 – Arithmetic Mean N – Number of cases
𝑀0 – Midpoint of origin
C – Class interval
σ 𝑓𝑑 – Sum of the frequency times the deviation
24. MEAN CLASS-DEVIATION METHOD
To apply the formula, consider the steps follows:
1. Choose any of the temporary arbitrary origin from any
of the class limits either at the bottom, at the center, or
at the top.
2. Assign to class limits coded values starting with zero at
the origin and above zero deviation is positive values
and below it, negative. The deviation (d) appears in
Column 4.
25. MEAN CLASS-DEVIATION METHOD
3. Multiply the deviation (d) by the frequency (f) to get fd.
The products are shown in Column 5.
4. Sum the products of fd algebraically. The symbol is
σ 𝑓𝑑.
5. Compute the mean using the formula of the class-
deviation method.
30. MEDIAN
Median is another measure of central tendency commonly
used by classroom teachers. Median is defined as point in
a scale such that the scores above and below it lie 50
percent (50%) of the cases. It may or may not stand for a
score.
31. MEDIAN FROM GROUPED DATA
Median from grouped data in a form of frequency
distribution is applicable when the number of cases is 30
or more. The concept is to determine a value that falls 50
percent (50%) above and the other half below it.
32. MEDIAN FROM GROUPED DATA
Median from Below:
1. Estimate the cumulative frequencies “lesser than” CF<
presented in Column 3.
2. Look for N/2 or one-half of the cases in the distribution.
3. Determine the class limit which the 25th case falls.
4. Look for the L or lower real limit of the median class,
frequency of the median class (fc), and sum of the
cumulative frequency “lesser than” up to below the median
class (σ 𝐶𝑓 <).
33. MEDIAN FROM GROUPED DATA
Median from Below:
5. Compute the median from below by using this formula:
෨
𝑋 = 𝐿 + 𝐶
𝑁
2
−σ 𝐶𝑓<
𝑓𝑐
Where: ෨
𝑋 – Median
L – Lower real limit , N – Number of cases
C – Class interval
34. MEDIAN FROM GROUPED DATA
Median from Below:
5. Compute the median from below by using this formula:
෨
𝑋 = 𝐿 + 𝐶
𝑁
2
−σ 𝐶𝑓<
𝑓𝑐
Where: σ 𝐶𝑓 < – sum of the cumulative frequency “lesser
than” up to but below the median class
fc – frequency of the median class
37. MEDIAN FROM GROUPED DATA
Median from above:
Median from above in a form of frequency distribution has
the same value with median from below. But cumulative
frequency “greater than” is used. The formula of median
from above is as follows:
෨
𝑋 = 𝑈 − 𝐶
𝑁
2
−σ 𝐶𝑓>
𝑓𝑐
38. MEDIAN FROM GROUPED DATA
෨
𝑋 = 𝑈 − 𝐶
𝑁
2
−σ 𝐶𝑓>
𝑓𝑐
Where: ෨
𝑋 – Median
U – Upper real limit
C – Class interval
N – Number of cases
39. MEDIAN FROM GROUPED DATA
෨
𝑋 = 𝑈 − 𝐶
𝑁
2
−σ 𝐶𝑓>
𝑓𝑐
Where: σ 𝐶𝑓 > – Sum of the cumulative frequency
“greater than” up to but above the
median class
fc – Frequency of the median class
42. MODE FROM GROUPED DATA
Mode from grouped data in a form of frequency
distribution is applicable when the number of cases (N) is
30 or more. The modal class is found in a class limit having
the highest frequency. If there are two class limits with the
same highest frequency, hence there are two modes; if
three, trimodal; and if four or more, polymodal.
43. MODE FROM GROUPED DATA
To get the mode from grouped data, consider the
following:
𝑋 = 𝐿𝑚𝑜 +
𝐶
2
𝑓1−𝑓2
𝑓0−𝑓2−𝑓1
Where
𝑋 − Mode
𝐿𝑚𝑜 − Lower real limit of the modal class
44. MODE FROM GROUPED DATA
To get the mode from grouped data, consider the
following:
𝑋 = 𝐿𝑚𝑜 +
𝐶
2
𝑓1−𝑓2
𝑓0−𝑓2−𝑓1
Where C – Class interval
𝑓0 – frequency of the modal class
𝑓1 – frequency after the modal class
𝑓2 – frequency before the modal class
