Advanced Mathematics Program 8

Prepared by: Ms. Lady Asrah A. Carim

Burger, Ice Cream and Hotdog:
What’s the most liked food?
•How many among you like Burger the most?
•How many like Ice Cream?
•How many like Hotdog?
•How many don’t eat neither of the foods
above?

Gender Burger Ice Cream Hotdog Neither TOTAL
Boys IIII IIII III I 13
Girls IIII - II IIII I 12
TOTAL 11 9 4 1 25

0
2
4
6
8
Burger Ice Cream Hotdog Neither
NumberofStudents
Foods
Most Liked Food by the Grade 8 Students
(Between Burger, Ice Cream and Hotdog)
Boys
Girls

•How did you collect the data?
•Why do you think it is needed to organize
data?
•Why is it important to present data?
Answer the following questions
based on the activity:

Advanced Mathematics Program 8

Statistics
•In singular, it refers to the branch
of mathematics which deals with
systematic collection, tabulation,
presentation, analysis and
interpretation of quantitative data
which are collected in a
methodical manner without bias.

Statistics
•In plural, it is defined
as a set of quantitative
data or facts.

Statistics
•In general sense of the word,
statistics deals on statistical
methods that refer to the
procedure and techniques used in
the collection, presentation,
analysis and interpretation of
quantitative data.

Statistics
•Moreover, it is the language of
research.
•Research without Statistics has no
language or meaning of the results
because Statistics give both
qualitative and quantitative
interpretation.

ScopeofStatistics
• Biological Sciences
• Economics
• Commerce, Trade and Industry
• Education
• Engineering
• Fisheries
• Agriculture
• Health, Nursing and Medicine
• Chemistry

Biological Sciences
• Statistical techniques are of vital importance in
evaluating, analyzing, and interpreting experiments.
• E.g., observing butterfly metamorphosis
Economics
• The supply and demand of commodities need statistical
analysis and interpretation for better understanding.
• E.g., before investors put up businesses here, they study
our economical status through the records collected.

Commerce, Trade and Industry
•Statistical techniques are of vital importance in
planning, production, and marketing of
commodities, prices, costs, and profits.
•E.g., you will determine if your business is going to
be successful based on the ups and downs of sales.
Education
•Statistics is vital tool in evaluating the achievements
of students and performance of teachers, staff, and
administrators.
•E.g., determining who gets 99+ in CEM is Statistics.

Engineering
•Statistics is necessary in the construction of
buildings, roads, and bridges.
•E.g., to determine which products are the most
durable, which building design is most demanded,
engineers use Statistics.
Fisheries
•Statistics is used in the analysis and interpretation of
experimental data.
•E.g., to study the environment before raising fishes,
they study the water if they’re safe or not.

Agriculture
• Statistical treatment is widely used in the analysis and interpretation of
data in their experiments and in agricultural economy.
• E.g., they use Statistics in studying soil quality.
Health, Nursing and Medicine
• In this field, statistics is an indispensable tool. Determination f the
effectiveness of treatment is based on a collection of records of clinical
trials where valid conclusions can be drawn.
• E.g., to determine the effectiveness of a medicine, they conduct a survey
to their patients.
Chemistry
• Statistical analysis and interpretation of data of their experiments are
needed to arrive at valid and reliable results.
• E.g., observing the characteristics of any element, they use statistics.

• S cientific
• T alented
• A ctive
• T enacious
• I nnovative
• S killful
• T errific
• I nventive
• C reative
• I nterpretative
• A ccurate
• N oble
Qualities of a Good STATISTICIAN

• He is precise and exact in collecting, presenting,
analyzing and interpreting the quantitative data.
• He uses the appropriate or correct statistical tool
for every research problem to arrive at valid results.
Scientific
• He has a great ability in any fields of endeavor.
• In other words, he has a well-rounded personality.
Talented

• He participates in all activities in school and in the
community efficiently, effectively and economically.
Active
• He is not forgetful.
• He can quickly memorize and recall different
statistical formulae and steps to compute them.
Tenacious
• He introduces new research works.
• He does not copy the works of others.
Innovative

• He is skilled or expert in computing the
statistical formulae.
Skillful
• He has extraordinary abilities wherein others
cannot cope with his abilities and talents.
Terrific
• He invents original and productive works that
can contribute to the economic recovery of the
country.
Inventive

• He utilizes indigenous or waste materials into useful
things.
Creative
• He interprets the research results correctly.
Interpretative
• He computes the different statistical tools correctly.
Accurate
• He has excellent and superior ability.
Noble

In a 1/4 sheet of paper, answer the
question NEATLY and INFORMATIVELY.
•Of the 12 qualities of a good
statistician, give three qualities that
you best possess and explain.

LONG QUIZ on Monday, about:
•Meaning of Statistics
•Scope of Statistics
•Qualities of a Good Statistician
Note: Please prepare one half sheet (lengthwise) of intermediate paper before I
enter the class.

Quantitative data collected from set of
measurements such as tests and
experiments’ results should be
classified, TABULATED, analyzed and
interpreted by investigators. These
data should be grouped in a
systematic order in a form of
FREQUENCY DISTRIBUTION.

•is any arrangement of the data that
shows the frequency occurrences of
different values of the variable or the
frequency of the occurrence of values
fall within arbitrarily defined ranges of
variable known as class limit.
•It is applied only if the total number of
cases (N) is equal to or greater than 30.
Frequency Distribution

•There are 40 second year high
school students in TQA who took
the first grading in Mathematics
test. The total number of items in
the test is 120. The scores was
107, 90, 88, 74, 55, 46, 30, and
so on.
Example:

41 73 102 81
42 70 38 88
30 62 43 63
35 50 90 52
57 90 56 59
100 80 46 107
99 55 71 100
55 75 74 90
43 63 75 68
98 69 68 67
Scores of 40 Grade 8 Students in Mathematics in TQA

Steps to Construct a Frequency Distribution
Table:
• Find the Range. R = Highest Score – Lowest Score
• Find the Class Interval (C) – In getting the class interval, we
simply divide the R by 10 and 20. Round off. And pick the
highest odd number that is not greater than 10.
• Set up the Classes. (Real Limit and Integral Limit). For the real
limit (or exact limit, or class boundaries), add and subtract
C/2 to the highest number to set the highest class limit. To
get the Integral Limit, add and subtract 0.5 to the class
limits. Continue setting up the classes by subtracting C from
each limit.
• TALLY THE SCORES and find the frequency by adding the
tallied scores.

40 55 43 47 45
65 70 78 75 70
55 69 50 75 63
77 47 50 66 43
63 82 80 71 55
67 68 76 70 58
50 84 73 51 64
65 49 79 66 68
Above are the weights in kilograms by group of 40 high school students.
Set the classes in real and integral limits. Choose the most appropriate
class interval.

• This is needed to determine the number of
values “greater than (>)” or “lesser than (<)” a
specified value. Such data may be readily seen in
a cumulative frequency distribution.
• In this, interest may center on the frequency of
values greater than the lower limit of any class or
on those less than the upper limit of a class.
• These are obtained by cumulative or successively
adding the individual frequencies starting either
from the bottom of “<“ or at the top of “>”.
Cumulative Frequency Distribution

•Obtained by dividing the cumulative frequency is obtained
by dividing the cumulative frequency by the total number of
(N) times 100, shows the percent of students falling below
or above (CPF< or CPF>) certain score values.
•The formula is CPF = (CF/N) x 100
Cumulative Percentage Frequency Distribution

These answer the
questions..
How many Grade 8 students got scores
lower than 75?
How many students got scores higher than
83?
What percent of the class got a score higher
than 34?
What percent of the class got a score lower
than 96?

Class Limit F CF < CF > CPF < (in %) CPF > (in %)
104 - 110 1
97 – 103 5
90 – 96 3
83 – 89 2
76 – 82 2
69 – 75 7
62 – 68 6
55 – 61 4
48 – 54 2
41 – 47 5
34 – 40 2
27 -33 1
40

104 - 110 1 40
97 – 103 5 39
90 – 96 3 34
83 – 89 2 31
76 – 82 2 29
69 – 75 7 27
62 – 68 6 20
55 – 61 4 14
48 – 54 2 10
41 – 47 5 8
34 – 40 2 3
27 -33 1 1
40

104 - 110 1 40 1
97 – 103 5 39 6
90 – 96 3 34 9
83 – 89 2 31 11
76 – 82 2 29 13
69 – 75 7 27 20
62 – 68 6 20 26
55 – 61 4 14 30
48 – 54 2 10 32
41 – 47 5 8 37
34 – 40 2 3 39
27 -33 1 1 40
40

104 - 110 1 40 1 100.0
97 – 103 5 39 6 97.5
90 – 96 3 34 9 85.0
83 – 89 2 31 11 77.5
76 – 82 2 29 13 72.5
69 – 75 7 27 20 67.5
62 – 68 6 20 26 50.0
55 – 61 4 14 30 35.0
48 – 54 2 10 32 25.0
41 – 47 5 8 37 20.0
34 – 40 2 3 39 7.5
27 -33 1 1 40 2.5
40

104 - 110 1 40 1 100.0 2.5
97 – 103 5 39 6 97.5 15.0
90 – 96 3 34 9 85.0 22.5
83 – 89 2 31 11 77.5 27.5
76 – 82 2 29 13 72.5 32.5
69 – 75 7 27 20 67.5 50.0
62 – 68 6 20 26 50.0 65.0
55 – 61 4 14 30 35.0 75.0
48 – 54 2 10 32 25.0 80.0
41 – 47 5 8 37 20.0 92.5
34 – 40 2 3 39 7.5 97.5
27 -33 1 1 40 2.5 100.0
40

Using the set of data and the frequency distribution
table you constructed (the correct one), get the
values of the CF <, CF >, CPF <, and CPF >.

Graph
•It is a geometrical image or a
mathematical picture of a set of
data.
•For this purpose, line graph
and a bar graph is commonly
used.

Line Graph
•It is a graph in which the frequencies
are plotted with a dot at their
midpoints and connecting the plotted
points by means of straight lines.
•To obtain the midpoint, simply add
the lower and the upper limits and
divide the sum by two.

Class Limit F Midpoint CF < CF >
104 - 110 1 107 40 1
97 – 103 5 100 39 6
90 – 96 3 93 34 9
83 – 89 2 86 31 11
76 – 82 2 79 29 13
69 – 75 7 72 27 20
62 – 68 6 65 20 26
55 – 61 4 58 14 30
48 – 54 2 51 10 32
41 – 47 5 44 8 37
34 – 40 2 37 3 39
27 -33 1 30 1 40
40
Frequency Distributions with Midpoints of the Mathematics Test Taken
by Forty Second Year High School Students in TQA

1
2
5
2
4
6
7
2 2
3
5
10
1
2
3
4
5
6
7
8
30 37 44 51 58 65 72 79 86 93 100 107
Frequency
Midpoint
Line Graph of the Mathematics Test Taken by Forty
Second High School Students in TQA

0
2
4
6
8
104 - 110 97 – 103 90 – 96 83 – 89 76 – 82 69 – 75 62 – 68 55 – 61 48 – 54 41 – 47 34 – 40 27 -33
Frequenciy
Class Interval
Frequency Distributions with Midpoints of the
Mathematics Test Taken by Forty Second Year High School
Students in TQA

Cumulative Frequency Line Graph/Ogive
•The plotting of cumulative frequency line graph
differs from that of a frequency line graph in two
ways:
•First, plot the dots corresponding to cumulative
frequencies.
•Second, plot the dots above the top of the upper
class limits.
•This is done to visualize whether the graph
represents the number of cases falling above and
below the particular values.

1
3
8
10
14
20
27
29
31
34
39 4040 39
37
32
30
26
20
13
11
9
6
1
0
5
10
15
20
25
30
35
40
45
CF<andCF>
Class Interval
Ogive of the Mathematics Test Taken by Forty Second High
School Students in TQA
CF < CF >

Bar Graph
•This is a graph that the frequencies
are represented by areas in the
form of vertical rectangles or bars.
•Each bar draw with its base equal to
the midpoint of the class limit and
height corresponding to the
absolute frequency.

1
2
5
2
4
6
7
2 2
3
5
1
0
1
2
3
4
5
6
7
8
Frequency
Class Interval
Bar Graph of the Mathematics Test Taken by Forty Second
High School Students in TQA

1
3
8
10
14
20
27
29
31
34
39 40
0
5
10
15
20
25
30
35
40
45
CF<
Class Interval
CF < Bar Graph of the Mathematics Test Taken by Forty

40 39
37
32
30
26
20
13
11
9
6
1
0
5
10
15
20
25
30
35
40
45
CF>
Class Interval
CF > Bar Graph of the Mathematics Test Taken by Forty

2.5
7.5
20
25
35
50
67.5
72.5
77.5
85
97.5 100
0
20
40
60
80
100
120
CPF<
Class Interval
CPF < Bar Graph of the Mathematics Test Taken by Forty

100 97.5
92.5
80
75
65
50
32.5
27.5
22.5
15
1.5
0
20
40
60
80
100
120
CPF>
Class Interval
CPF > Bar Graph of the Mathematics Test Taken by Forty

100 97.5 92.5
80 75
65
50
32.5 27.5 22.5
15
1.52.5 7.5
20 25
35
50
67.5 72.5 77.5
85
97.5 100
0
20
40
60
80
100
120
CPF>andCPF<
Class Interval
CPF > and CPF > Bar Graph of the Mathematics Test Taken
by Forty Second High School Students in TQA
CPF < CPF >

• Line Graph gives a better picture of a distribution.
• The change of points from one place to another is
direct and fives correct impression.
• It is advantageous also in plotting two or more sets of
distribution overlapping on same baseline because it
still gives a clear picture of the comparison of each
distribution.
Advantages of Line Graph

Advanced Mathematics Program 8

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