3. Mean
• The most reliable and the most
sensitive measure of position.
• It is the most widely used
measure.
• It is commonly known as the
“average” although the median and
the mode are also known as
averages.
4. Mean:
• It comes into 2 different
forms:
1) Simple Mean
2) Weighted Mean
5. Example 1:
A study was done on 5 typical fast-food
meals in Metro Manila. The following table
shows the amount of fat, in number of
teaspoons, present in each meal. Calculate
the mean amount of fat for these 5 fast-
food meals.
Fast-food meal A B C D E
Fat (in tsp) 14 18 22 10 16
6. How to solve the simple
mean:
• The simple mean is obtained by
adding all the values/
observations of a certain
variable and divide the sum by
the total number of values,
cases or observations.
7. • To obtain the simple mean amount
of fat for the 5 fast-food meals
• Mean = (14+18+22+10+16)/5
• Mean = 80/5 = 16
• This means to say that mean fat
content of the 5 fast-food meals
is too much.
Fast-food meal A B C D E
Fat (in tsp) 14 18 22 10 16
8. Exercise #2: Find the simple
mean for the following set of data:
• Data A: 17, 19, 25, 14,
18, 24, 11,19
• Data B: 79, 75, 82, 84,
82, 75, 79
• Data C: 35, 32, 37, 42, 45,
33, 41, 44, 35, 38
9. The simple mean for the
given data are …
• Data A: 18.38
• Data B: 79.43
• Data C: 38.20
10. Example 2:
• The following represents the final
grades obtained by a nursing
student one summer term:
• Anatomy (5 units) - - - 93
• Chemistry (3 units) - - - 88
• SOT 2 (2 units) - - - 89
– Find the weighted average of the
student.
11. To solve for the weighted average
of the student we have...
wixi
Mean = ----------
w
93(5) + 88(3) + 89(2)
Mean = --------------------------
10
465 + 264 + 178 907
Mean = ----------------------- = -------- = 90.7 (Excellent)
10 10
12. Example 3:
• The following represents the responses of
50 randomly chosen respondents in one
item of a research questionnaire:
• Very Strongly Agree (5) - - - 17
• Strongly Agree (4) - - - 11
• Agree (3) - - - 9
• Disagree (2) - - - 12
• Strongly Disagree (1) - - - 1
– Find the weighted response of the
respondents.
13. To solve for the weighted
response we have...
wixi
Mean = ----------
w
5(17) + 4(11) + 3(9) + 2(12) + 1(1)
Mean = ------------------------------------------
50
85+44+27+24+1 181
Mean = ----------------------- = -------- = 3.62 (Strongly Agree)
50 50
16. The median is . . .
• A positional measure that divides
the set of data exactly into two
parts.
• It is the score/observation that is
centrally located between the
highest and the lowest observation.
• Determined by rearranging the data
into an array.
17. n + 1
X = -------
2
n n
X = --- + --- + 1
2 2
--------------
2
Median for Odd Sample Median for Even Sample
18. Using the data
in Example 1,
find the
median fat
content of the
5 meals.
19. Example 1:
A study was done on 5 typical fast-food
meals in Metro Manila. The following table
shows the amount of fat, in number of
teaspoons, present in each meal. Calculate
the mean amount of fat for these 5 fast-
food meals.
Fast-food meal A B C D E
Fat (in tsp) 14 18 22 10 16
21. The array for the data A is :
10, 14, 16, 18, 22
• To obtain the median fat
content of the 5 meals we have
to use the median formula for
odd sample since n = 5.
• Median = [(n + 1)/2]s
• Median = (5 + 1)/2
• Median = 3rd item = 16
26. The mode is …
The most favorite score.
The score having the highest
frequency.
The most frequently occurring score.
The least reliable measure of position
Determined by way of inspection.
27. A set of data is said to
be …
• Unimodal or monomodal if it
has only one mode.
• Example: 33, 35, 35, 38,
40, 46
• Its mode is 35.
28. A set of data is said to
be …
• Bimodal if it has two modes.
• Example: 33, 35, 35, 38,
40, 40, 46
• Its modes are 35 and 40.
29. A set of data is said to be …
• Multimodal if it has more than
two modes.
• Example: 33, 35, 35, 38, 40,
40, 46, 46, 51, 58, 58, 60
• Its modes are 35, 40, 46 and
58.
30. Assignment #1: Find the mean,
median and the mode of the ff:
1. 85, 82, 83, 88, 85, 87, 89,
90
2. 12, 14, 20, 19, 23, 22, 28
3. 24, 34, 27, 27, 34, 24
4. 102, 100, 111, 100, 106, 102
5. 75, 86, 78, 84, 88, 86, 84,
85, 81, 84, 80
32. What is a Frequency
Distribution?
• A Frequency
Distribution is a tabular
representation of data
consisting of intervals
and their respective
frequencies.
38. How to construct a
Frequency Distribution:
• Determine the range. R = H0 –
LO.
• Determine the class size (c) using
the formula, c = (R+1)/ #CI.
• Construct the interval
• Tally the data and determine the
frequency for each interval.
39. The class interval in a
frequency distribution must:
• Not overlap.
• Be relatively complete where
each data can be tallied in the
different interval.
• Have a uniform class size.
• Not be less than 7 but not
more than 15.
46. C (n/2 -CF<)
Median = Lbe + -----------------
fm
Where: Lbe is the lower boundary of the median class
C is the class size
fm is the frequency of the median class
CF< is the cumulative frequency less than before
the median class
Median Class is the class interval containing half of n
48. C (d1)
Mode = Lbo + ------------
(d1 + d2 )
Where: Lb0 is the lower boundary of the modal class
d1 is the difference in the frequency of the modal
class with the frequency of the class interval
before the modal class
d2 is the difference in the frequency of the modal
class with the frequency of the class interval
after the modal class
Modal Class is the class interval with the highest frequency
54. The Mean is used…
For interval and ratio measurements
When there are no extreme values in a
distribution since it is easily affected by
extremely high or extremely low scores
When higher statistical computations are
wanted
When the greatest reliability of the
measure of central tendency is wanted
since its computations include all the given
values
55. The Median is used…
For ordinal and ranked measurements
When there are extreme values, thus the
distribution is markedly skewed
For an open-end distribution; that is, the
lowest or the highest class interval or both
are defined (i.e., 50 and below or 100 and
above)
When one desires to know whether the
cases fall within the upper halves or the
lower halves of a distribution.
56. The Mode is used…
For nominal and categorical data
When a rough or quick estimate of a
central value is wanted
When the most popular or the most
typical case or value in a distribution
is wanted
58. The Limitations of the Mean…
It is the most widely used average, since it
is the most familiar. However, it is often
misused. It can not be used if the
clustering of values. Or items is not
substantial.
If the given values do not tend to cluster
around a central value, the mean is a poor
measure of central location.
It is easily affected by extremely large or
small values. One small value can easily pull
down the mean.
59. The Limitations of the Mean…
The mean can not be used to compare
distributions since the means of 2 or more
distributions may be the same but their
other characteristics may be entirely
different. The means of distribution A
whose values are 80, 85 and 90 and
distribution B whose values are 86, 85, 84
are both 85. We can not imply, however,
that both distributions possess the same
characteristics since their patterns of
dispersions or variations are markedly
different despite having the same mean.
60. The Limitations of the Median…
It is easily affected by the number of
items in a distribution.
It can not be determined if the given values
are not arranged according to magnitude
If several values are contained in a
distribution, it becomes laborious task to
arrange them according to magnitude
Its value is not as accurate as the mean
since it is just an ordinal statistic.
61. The Limitations of the Mode…
It is seldom or rarely used since it
does not always exist.
Its value is just a rough estimate of
the center of concentration of a
distribution.
It is very unstable since its value
easily changes depending on the
approaches used in finding it.
62.
63. Measures of Variability
• The statistical tool used to
describe the degree to
which scores/ observations
are scattered/dispersed.
• It is also used to determine
the degree of consistency/
homogeneity of scores.
66. The following are the scores obtained by
two groups of 2nd year ASHE students in
N101:
Group A
30
28
27
25
25
23
21
20
18
12
Group B
30
20
18
16
15
15
14
13
12
12
67. X |X - Mean| (X - Mean)
2
30 7.1 50.41
28 5.1 26.01
27 4.1 16.81
25 2.1 4.41
25 2.1 4.41
23 0.1 0.01
21 1.9 3.61
20 2.9 8.41
18 4.9 24.01
12 10.9 118.81
22.9 41.2 256.9
G
R
O
U
P
A
Range = 30 – 12 = 18
Standard dev’n =
256.9/(10-1)
= 28.54
= 5.34
Mean Dev’n = 41.2/10
= 4.12
Variance = (5.34)2
= 28.54
CV = (5.34/22.9) X 100
= 23.32%
70. Problem:
Two seemingly equally excellent BSN
students are vying for an academic
honor where only one must have to be
chosen to get the award. The
following are their grades used as
basis for the award:
Franzen : 91, 90, 94, 93, 92
Rico : 92, 92, 90, 94, 92
Whom do you think deserves to get
the award?
71. Guiding Principle
The lesser the value of the
measure, the more consistent,
the more homogeneous and
the less scattered are the
observations in the set of
data.
