FLORINDA M SOLIMAN TEACHER II TAGAYTAY CITY SCIENCE NATIONAL HIGH SCHOOL.
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FLORINDA M SOLIMAN TEACHER II
TAGAYTAY CITY SCIENCE NATIONAL
HIGH SCHOOL
A measures of central tendency may be defined as single expression of the net result of a complex group.
There are two main objectives for the study of measures of Central Tendency.
To facilitate comparison
To get one single value that represents the entire data.
There are three averages or measures of central tendency
Mean
Median
Mode
Mean/Arithmetic Mean The most commonly used and familiar index of
central tendency for a set of raw data or a distribution is the mean
The mean is simple Arithmetic Average
The arithmetic mean of a set of values is their sum divided by their number
MERITS OF THE USE OF MEAN
It is easy to understand
It is easy to calculate
It utilizes entire data in the group
It provides a good comparison
It is rigidly defined
Limitations
Abnormal difference between the highest and the lowest score would lead to fallacious conclusions
In the absence of actual data it can mislead
Its value cannot be determined graphically
A mean sometimes gives such results as appear almost absurd. e.g. 4.3. children
Steps in Constructing Frequency Distribution Table
1. Range = Highest Score – Lowest Score
2. Class Width =
49
4844
4746
44
4640
4340
40
4241
4136
36
3637
3738
38
3939
3932
32
3232
3333
33
3435
34
35
28
28
28
2929
29
2929
3030
25
2424
2525
26
2727
2021
22
2321
2222
23
2316
1617
19
1213
1415
12
8 8 8 8 9 10 7 7 7
49
4844
4746
44
4640
4340
40
4241
4136
36
3637
3738
38
3939
3932
32
3232
3333
33
3435
34
35
28
28
28
2929
29
2929
3030
25
2424
2525
26
2727
2021
22
2321
2222
23
2316
1617
19
1213
1415
12
8 8 8 8 9 10 7 7 7
CLASS INTERVALS ( CI ) FREQUENCY ( F )
n 80
48 – 51
n 80
44 – 47
80
40 – 43
80
36 – 39
80
32 – 35
n 80
28 – 31
80
24 – 27
80
20 – 23
80
16 – 19
n 80
12 – 15
80
8 – 11
n 80
4 – 7
n 80
CLASS INTERVALS ( CI ) FREQUENCY ( F )
n 80
48 – 512
n 80
44 – 47 5
40 – 43 7
80
36 – 39 10
80
32 – 35 11
n 80
28 – 31 10
80
24 – 27 8
80
20 – 23 9
80
16 – 19 4
n 80
12 – 15 5
80
8 – 11 6
n 80
4 – 7 3
n 80
Calculation for Mean
Calculation of Arithmetic MeanFor Group DataAssume mean Method:
Mean = AM +
Calculation of Arithmetic MeanFor Group Data
X = midpoint
AM = Assumed Mean
i = Class Interval size
fd = Product of the frequency and the
corresponding deviation
Class Intervals
( CI )
Frequency ( F )
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4
12 – 15 5
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 – 23 9
16 – 19 4
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2
44 – 47 5
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52
44 – 47 5 78
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80
44 – 47 5 78
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80
44 – 47 5 78
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35 25.5
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18 17.5
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18 17.5
12 – 15 5 14 13.5
8 – 11 6 9
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18 17.5
12 – 15 5 14 13.5
8 – 11 6 9 9.5
4 - 7 3 3
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18 17.5
12 – 15 5 14 13.5
8 – 11 6 9 9.5
4 - 7 3 3 5.5
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5
44 – 47 5 78 45.5
40 – 43 7 73 41.5
36 – 39 10 66 37.5
32 – 35 11 56 33.5
28 – 31 10 45 29.5 0
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18 17.5
12 – 15 5 14 13.5
8 – 11 6 9 9.5
4 - 7 3 3 5.5
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5 5
44 – 47 5 78 45.5 4
40 – 43 7 73 41.5 3
36 – 39 10 66 37.5 2
32 – 35 11 56 33.5 1
28 – 31 10 45 29.5 0
24 – 27 8 35 25.5
20 - 23 9 27 21.5
16 – 19 4 18 17.5
12 – 15 5 14 13.5
8 – 11 6 9 9.5
4 - 7 3 3 5.5
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5 5
44 – 47 5 78 45.5 4
40 – 43 7 73 41.5 3
36 – 39 10 66 37.5 2
32 – 35 11 56 33.5 1
28 – 31 10 45 29.5 0
24 – 27 8 35 25.5 -1
20 - 23 9 27 21.5 -2
16 – 19 4 18 17.5 -3
12 – 15 5 14 13.5 -4
8 – 11 6 9 9.5 -5
4 - 7 3 3 5.5 -6
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’
48 – 52 2 80 49.5 5
44 – 47 5 78 45.5 4
40 – 43 7 73 41.5 3
36 – 39 10 66 37.5 2
32 – 35 11 56 33.5 1
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1
20 - 23 9 27 21.5 -2
16 – 19 4 18 17.5 -3
12 – 15 5 14 13.5 -4
8 – 11 6 9 9.5 -5
4 - 7 3 3 5.5 -6
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5 5 10
44 – 47 5 78 45.5 4 20
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1
20 - 23 9 27 21.5 -2
16 – 19 4 18 17.5 -3
12 – 15 5 14 13.5 -4
8 – 11 6 9 9.5 -5
4 - 7 3 3 5.5 -6
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5 5 10
44 – 47 5 78 45.5 4 20
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5 5 10
44 – 47 5 78 45.5 4 20
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80 -24
Class Intervals
( CI )
Frequency ( F ) <Cf Mdpt d’ fd’
48 – 52 2 80 49.5 5 10
44 – 47 5 78 45.5 4 20
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80 -24
Calculation for Median
Median
When all the observation of a variable are arranged in either ascending or descending order the middles observation is Median. It divides the whole data into equal proportion. In other words 50% observations will be smaller than the median and 50% will be larger than it.
Merits of Median
Like mean, Median is simple to understand
Median is not affective by extreme items
Median never gives absurd or fallacious result
Median is specially useful in qualitative
phenomena
Median = L +
Where,L = exact lower limit of the Cl in which
Median lies
F = Cumulative frequency up to the lower limit of the Cl containing Median
fm = Frequency of the Cl containing median
i = Size of the class intervals
Class Intervals( CI )
Frequency ( F )<Cf
48 – 52 2 80
44 – 47 5 78
40 – 43 7 73
36 – 39 10 66
32 – 35 11 56
28 – 31 10 45
24 – 27 8 35F
20 - 23 9 27
16 – 19 4 18
12 – 15 5 14
8 – 11 6 9
4 - 7 3 3
Total 80
28 – 31 10 45
35F
10 fm
Median = L +
Here; L = 27.5 F = 35 fm =10
= 27.5 + (40 – 35) 10 4
= 27.5 + 2
= 29.5
MARILOU M. MARTINTEACHER - 1
IMUS NATIONAL HIGH SCHOOL
The goal for variability is to obtain a measure
of how spread out the scores are in a distribution.
A measure of variability usually accompanies
a measure of central tendency as basic
descriptive statistics for a set of scores.
Central tendency describes the central point
of the distribution, and variability describes
how the scores are scattered around that central point.
Together, central tendency and variability are
the two primary values that are used to describe a distribution of scores.
Variability serves both as a descriptive measure and as an important component of most inferential statistics.
As a descriptive statistic, variability measures the degree to which the scores are spread out or clustered together in a distribution.
In the context of inferential statistics, variability provides a measure of how accurately any individual score or sample represents the entire population.
When the population variability is small, all of the scores are clustered close together and any individual score or sample will necessarily provide a good representation of the entire set. On the other hand, when variability is large and scores are widely spread, it is easy for one or two extreme scores to give a distorted picture of the general population.
Variability can be measured with the rangethe interquartile rangethe standard deviation/variance.
In each case, variability is determined by measuring distance.
Standard deviation measures the standard distance between a score and the mean. The calculation of standard
deviation can be summarized as a four-step process:
1. Compute the deviation (distance from the mean) for each score.
2. Solve for the product of frequency and deviation and solve for the total frequency deviation.
3. Compute for the sum of the product of frequency deviation square.(fd’²)
Class Intervals
( CI )
Frequency ( F ) <Cf
Mdpt
d’ fd’ (fd’)²
48 – 52 2 80 49.5 5 10
44 – 47 5 78 45.5 4 20
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80 -24
Class Intervals
( CI )
Frequency ( F ) <Cf
Mdpt
d’ fd’ (fd’)²
48 – 52 2 80 49.5 5 10 50
44 – 47 5 78 45.5 4 20
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80 -24
Class Intervals
( CI )
Frequency ( F ) <Cf
Mdpt
d’ fd’ (fd’)²
48 – 52 2 80 49.5 5 10 50
44 – 47 5 78 45.5 4 20 80
40 – 43 7 73 41.5 3 21
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80 -24
Class Intervals
( CI )
Frequency ( F ) <Cf
Mdpt
d’ fd’ (fd’)²
48 – 52 2 80 49.5 5 10 50
44 – 47 5 78 45.5 4 20 80
40 – 43 7 73 41.5 3 21 63
36 – 39 10 66 37.5 2 20
32 – 35 11 56 33.5 1 11
28 – 31 10 45 29.5 0 0
24 – 27 8 35 25.5 -1 -8
20 - 23 9 27 21.5 -2 -18
16 – 19 4 18 17.5 -3 -12
12 – 15 5 14 13.5 -4 -20
8 – 11 6 9 9.5 -5 -30
4 - 7 3 3 5.5 -6 -18
Total 80 -24
Class Intervals
( CI )
Frequency ( F ) <Cf
Mdpt
d’ fd’ (fd’²)
48 – 52 2 80 49.5 5 10 50
44 – 47 5 78 45.5 4 20 80
40 – 43 7 73 41.5 3 21 63
36 – 39 10 66 37.5 2 20 40
32 – 35 11 56 33.5 1 11 11
28 – 31 10 45 29.5 0 0 0
24 – 27 8 35 25.5 -1 -8 8
20 - 23 9 27 21.5 -2 -18 36
16 – 19 4 18 17.5 -3 -12 36
12 – 15 5 14 13.5 -4 -20 80
8 – 11 6 9 9.5 -5 -30 150
4 - 7 3 3 5.5 -6 -18 108
Total 80 -24 662
SD =
SD =
SD = 4 ( 2.879) = 11.52
SHIRLEY PEL – PASCUALMaster Teacher – I
GOV. FERRER MEMORIAL NATIONAL HIGH SCHOOL
Mean scores are used to determine the average performances of students or athletes, and in
various other applications. Mean scores can be converted to percentages that indicate the average percentage of the score relative to the total score.
Mean scores can also be converted to percentages to show the performance of a score relative to a specific score. For instance, a mean score can be compared to the highest score with a percentage for a better comparison. Percentages can be useful means of statistical analysis.
Instructions
1.Find the mean score if not already determined.
The mean score can be determined by adding
up all the scores and dividing it by "n," the number of scores.
Instructions
2 Determine the score that you want to compare the mean score to. You may compare the mean score with the highest possible score, the highest score, or a specific score.
Instructions
3. Divide the mean score by the score you decided to use in step 2.
Instructions
4. Multiply the decimal you obtain in step 3 by 100, and add a % sign to obtain the percentage. You may choose to round the percentage to the nearest whole number.
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