Advanced Mathematics Program 8

MEANING AND SCOPE OF STATISTICS

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?

GROUP ACTIVITYCollect:

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

Organize:

Burger Ice Cream Hotdog Neither01234567

Most Liked Food by the Grade 8 Stu-dents

(Between Burger, Ice Cream and Hotdog)

BoysGirls

Foods

Nu

mb

er

of

Stu

den

tsPresent:

• 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 questionsbased on the activity:

So, what is STATISTICS for you,based on our activity?

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.

Sco

pe o

f Sta

tist

ics • 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.

Scope of Statistics

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

QUALITIES OF A GOODS.T.A.T.I.S.T.I.C.I.A.N.

• 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.

Seat Work:

LONG QUIZ on Monday, about:

• Meaning of Statistics• Scope of Statistics• Qualities of a Good Statistician

Announcement:

Note: Please prepare one half sheet (lengthwise) of intermediate paper before I enter the class.

FREQUENCY DISTRIBUTION TABLE

Ms. Lady Asrah A. Carim

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 1028142 70 38 8830 62 43 6335 50 90 5257 90 56 59100 80 4610799 55 71 10055 75 74 9043 63 75 6898 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.

Assignment: On a whole sheet of yellow pad, make a Frequency Distribution Table for this set of data:

40 55 43 47 4565 70 78 75 7055 69 50 75 6377 47 50 66 4363 82 80 71 5567 68 76 70 5850 84 73 51 6465 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.

• 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 1028142 70 38 8830 62 43 6335 50 90 5257 90 56 59100 80 4610799 55 71 10055 75 74 9043 63 75 6898 69 68 67


Cumulative Frequency and Cumulative Percentage

FrequencyMs. Lady Asrah A. Carim

• 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



%)CPF > (in

%)

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



%)CPF > (in

%)

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



%)CPF > (in

%)

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



%)CPF > (in

%)

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


Assignment: 1YPUsing the set of data and the frequency distribution

table you constructed (the correct one), get the values of the CF <, CF >, CPF <, and CPF >.

Graphic Representation of

Frequency DistributionMs. Lady Asrah A. Carim

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

30 37 44 51 58 65 72 79 86 93 100 1070

1

2

3

4

5

6

7

8

1

2

5

2

4

6

7

2 2

3

5

1

Line Graph of the Mathematics Test Taken by Forty Second High School Students in

TQA

Midpoint

Fre

qu

en

cy

104 - 110 97 – 103 90 – 96 83 – 89 76 – 82 69 – 75 62 – 68 55 – 61 48 – 54 41 – 47 34 – 40 27 -33012345678

Frequency Distributions with Midpoints of the Mathematics Test Taken by Forty Second Year

High School Students in TQA

Class Interval

Fre

qu

en

ciy

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.

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

5

10

15

20

25

30

35

40

45

13

810

14

20

2729

3134

39 4040 3937

3230

26

20

1311

96

1

Ogive of the Mathematics Test Taken by Forty Second High School Students in TQA

CF < CF >

Class Interval

CF <

an

d C

F >

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.

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

1

2

3

4

5

6

7

8

1

2

5

2

4

6

7

2 2

3

5

1

Bar Graph of the Mathematics Test Taken by Forty Second High School Students in TQA

Class Interval

Fre

qu

en

cy

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

5

10

15

20

25

30

35

40

45

13

810

14

20

2729

3134

39 40

CF < Bar Graph of the Mathematics Test Taken by Forty Second High School Students in TQA

Class Interval

CF <

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

5

10

15

20

25

30

35

40

4540 39

37

3230

26

20

1311

96

1

CF > Bar Graph of the Mathematics Test Taken by Forty Second High School Students in TQA

Class Interval

CF >

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

5

10

15

20

25

30

35

40

45

13

810

14

20

2729

3134

39 4040 3937

3230

26

20

1311

96

1

Ogive of the Mathematics Test Taken by Forty Second High School Students in TQA

CF < CF >

Class Interval

CF <

an

d C

F >

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

20

40

60

80

100

120

2.57.5

2025

35

50

67.572.5

77.585

97.5 100

CPF < Bar Graph of the Mathematics Test Taken by Forty Second High School Students in TQA

Class Interval

CP

F <

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

20

40

60

80

100

120

100 97.592.5

8075

65

50

32.527.5

22.515

1.5

CPF > Bar Graph of the Mathematics Test Taken by Forty Second High School Students in TQA

Class Interval

CP

F >

27-33

34-40

41-47

48-54

55-61

62-68

69-75

76-82

83-89

90-96

97-103

104-110

0

20

40

60

80

100

120

100 97.5 92.580 75

65

50

32.5 27.5 22.515

1.52.5 7.520 25

35

50

67.5 72.5 77.585

97.5 100

CPF > and CPF > Bar Graph of the Mathematics Test Taken by Forty Second High School Students in TQA

CPF < CPF >

Class Interval

CP

F >

an

d C

PF <

• 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