essentiality of mathematics

STATISTICS SURVEY REPORT 1

PREPARED BY: 1. Muhammad Saeed 2. MUHAMMAD AAMIR RIAZ 3. Muhammad Imran

FACILITATOR: 1 MA’AM RAKHSHANDA SHAH

TOPIC: “ESSENTIALITY OF MATHEMATICS” COURSE: BUSSINESS MATHEMATICS DATE : 30TH MAY 2003


ACKNOWLEDGEMENT:

We, Muhammad Imran, Muhammad Aamir Riaz, Muhammad Saeed, worked in a group, to carry out a survey on “Essentiality Of Mathematics In Our Professional Life” which is also the requirement of this course, as this survey and the arrangement of data of this survey both are very time consuming & overshadowing effort but we thanks Almighty Allah who empowered us to complete these practical and report.

We would also like to say coordinal thanks and appreciate the memorable behaviour and loving attitudes of all the students of TIP to whom we have given the survey forms and in this regard their cooperation was beyond our expectations and this, helped us a lot in gratifying the data & accomplishment of this report.

We wish to elegantly and heartily thank to the instructor of our course, Ma’am Rakshanda Shah for his complete collaboration and assistance.

Responsibility for any sort of errors and exclusions is certainly our.


TOPIC: “Evolutionary study for the ignorance and fear of mathematics

in designing, management and textile science students.” As it is a very famous saying;

“Math is a way for lazy people to learn how to do thing quickly and well.”

“It’s a way to have a well organized mind and it will help you

to solve all kinds of problems later on in your age”.

PURPOSE OF STUDY: Our objective is to find the opinion of students about the essentiality of mathematics for professional field. My report is concerned with the feed back of students about the essentiality and the interest of mathematics in their professional field. The foremost objective is to compare the interest in mathematics between designing, management and textile science and also comparison between those students who likes and those who dislike the mathematics and their marks in exams.

QUESTIONNAIRES: Questionnaires can be most simply defined as apprises of collecting such information, from desired individuals groups or organizations, which cannot be easily obtained from direct sources.

“OR” The word questionnaires are used most often to describe a method of gathering information from a sample of individuals. This sample is usually just a fraction of the population being studied.


Assignment of statistics Evaluate yourself as a mathematician Name: ________________________ Sex: __________________________ class: __________ Age: _________________________ year: ___________ Discipline: Textile science Designing Management 1 Your marks in math’s in intermediate Less then 60 60-70 70-80 80-90 Above 90 2 Is mathematics is essential for your professional field? Yes NO 3 Do you like mathematics? Yes NO 4 What do you think that what is your level of mathematics? Low High Moderate 5 Is mathematics hard for you? YES NO 6 Your knowledge in maths is enough for daily life concerned. YES NO 7 You want to learn more maths. YES NO (if yes than tick Q#8) (If no than tick Q#9) 8 You like math’s due to

You found good teachers your parent’s guidance Your natural ability you don’t know 9 You fear by math’s due to You found not good teachers your don’t want to learn yourself You don’t find help from parents you don’t know

10 Regarding your ability in maths can you provide help to some one else? YES NO Respondent signature:__________


“SOME IMPORTANT DEFINITIONS” DEFINITION OF STATISTICS:

Statistics are numerical facts in any field of study. “OR”

Statistic deals with techniques or methods for collecting analyzing and drawing conclusions from data.

Statistics methods are divided into two categories namely descriptive and inferential.

2 Descriptive statistics 3 Inferential statistics

DESCRIPTIVE STATISTICS: It deals with the collections classifications summarization and presentation of data. INFERENTIAL STATISTICS: It deals with the conclusions drawn about a population using the data of a sample taken from the same population. POPULATION: Population consists of the totality of the observations with which we are concerned. SAMPLE: A sample is a subset of a population. SIMPLE RANDOM SAMPLE: A simple random sample of “n” observations is a sample that is chosen in such a way that very subset of n observations of the population has the same probability of being selected. PROBABILITY: A probability is a numeric measure of the likelihood or chance that a particular event will occur. Symbolically it is written as;


)()()(

SnAnAP =

It is further distributed into following ones; 1. Binomial 2. Poisson 3. Hyper geometric 4. Normal

MEASUREMENT OF TENDENCY: Generally we have two types of tendencies;

1. Measures of central tendency 2. Measures of dispersion

1. MEASURES OF CENTRAL TENDENCY: It is defined as a single value of the data, which truly represents the whole data. It is further classified into;

i. Arithmetic Mean ii. Geometric Mean

iii. Harmonic Mean iv. Median v. Mode

ARITHMETIC MEAN: It is the most commonly used measure and usually termed as simple mean. “It is defined as the sum of the values divided by the number

of values in the raw data.” Here the mean of a sample of n values, is known as sample mean and is denoted by x .

n

xx

n

ii∑

== 1

Whereas, if the data is not a sample but the entire population of N values, it is termed as population mean and is denoted by µ.

N

xN

ii∑

== 1µ

WEIGHTED ARITHMETIC MEAN: The mean of a data gives equal importance or weights to each of the values of raw data. In some general cases all values in the raw data

STATISTICS SURVEY REPORT 7 don’t have the same importance. A weighted mean is used to assign any degree of importance to each value of the data by choosing appropriate weights for these values.

∑∑=

wxw

xw

.

Here, “w” are the weights assigned to the values of data.

GEOMETRIC MEAN: Geometric mean is defined only for non-zero positive values. It is the nth root of the product of n values in the data.

Kn xxxG ...21=

WEIGHTED GEOMETRIC MEAN; If weights are assigned to the values of the data, in this regard we can calculate the geometric mean.

]log.

log[..∑

∑=w

xwAntiMG

HARMONIC MEAN: Harmonic mean is defined only for non-zero positive values; it is the reciprocal of mean of reciprocal of values.

∑=

= K

i ix

KH

1

1

WEIGHTED HARMONIC MEAN: If all values of the data are not equally important, a weighted harmonic mean is calculated after assigning appropriate weights to the values of the data.

∑∑=

)(..

xww

MH

MEDIAN: Median is defined as the middle value of the data when the values are arranged in ascending or descending order.

=µ~ ).2

( fcnfh

−+λ

STATISTICS SURVEY REPORT 8 MEDIAN OF A FREQUENCY DISTRIBUTION: Values of the data in an interval are evenly or uniformly spread in that interval is known as the median of the frequency distribution. PARTITION VALUES OR QUARTILES: QUARTILES: There are three values, which can divide the arranged data in four equal parts or quarters. These values are called quartiles.

).4

( fcnfhlQ i

i −+=

DECILES: There are nine values, which can divide the arranged data in ten equal parts.

).10

( fcnfhlD i

i −+=

PERCENTILES: Similarly, the 99 values, which divide the arranged data in 100 equal parts, are called percentiles.

).100

( fcnfhlP i

i −+=

MODE: Mode is a measure of central tendency generally used when the data is of qualitative nature where the addition (for mean) or arrangement (for median) of values is not possible. It is defined as that category of the attribute, which repeats maximum number of times in the data.

hfffm

ffmlxMode ×−−

−+== )

2121(ˆ

MODE OF A FREQUENCY DISTRIBUTION: In a frequency distribution mode is that value of the variable for which the frequency curve takes maximum height.

Width of the interval No. of values in the interval

STATISTICS SURVEY REPORT 9 A frequency distribution with one mode is called unimodal and with two modes is called a bimodal frequency distribution. 2. MEASURES OF DISPERSION: The dispersion is defined as the scatter or spread of the values from one another or from some common values. The method to compute the amount of dispersion present in any data is called “Measures of Dispersion” or “Measures of Variation”. The measures of dispersion are further classified into;

i. Range ii. Quartile Deviation

iii. Mean Deviation iv. Standard Deviation

RANGE: Range is the simple measure of dispersion and is defined as the differences between the maximum and minimum values of the data.

minmax XXR −=

Range is generally rough and crude measurement as it ignores the variation among all the values.

QUARTILE DEVIATION: The difference between the third and first quartiles is called the interquartile range and quartile deviation is the half of the interquartile range and is also known as the semi-interquartile range.

2.. 13 QQDQ −=

MEAN DEVIATION: Dispersion can be measured in terms of the quantities that each value of the data deviates from average value. Mean deviation for ungrouped data;

nxx

DM ∑ −=

||..

Mean deviation for grouped data;

∑

∑

=

=

−= K

ii

K

iii

f

xxfDM

1

1||

..

STATISTICS SURVEY REPORT 10 Hence in this regard it is defined as, sum of absolute deviations from mean divided by the number of values. STANDARD DEVIATION: Standard Deviation is the most widely used measure of dispersion and is defined as the positive square root of a quantity called variance. Standard deviation for sample-ungrouped data;

1

)(1

2

−

−=∑=

n

xxs

n

ii

Standard deviation for population-ungrouped data;

N

xN

ii∑

=

−= 1

2)( µσ

Standard deviation for sample-grouped data;

)1(

)(1 1

22

−

−=

∑ ∑= =

nn

xfxfns

K

i

K

iiiii

Standard deviation for population-grouped data;

N

xfxfNK

i

K

iiiii∑ ∑

= =

−= 1 1

22 )(σ


SAMPLING OF THE DATA:

POPULATION SAMPLE DEPARTMENT

M F

TOTAL

M F

TOTAL

Designing 12 39 51 8 25 33

Management 38 14 52 21 12 33

Science 130 3 133 31 2 34

Total 180 56 236 60 40 100

Here at TIP, after conducting this survey, we analyze that male in Science department are more proficient of learning Mathematics while in the Designing department female-heads are more engrossed and interested to learn mathematics as compare to the males.


Q#1: Your Marks In Mathematics In Intermediate? GENERAL DATA: This data is regarding to all the departments and on the ratio of the marks which the students got during their A levels or in their Intermediate.

MARKS IN MATH SCIENCE DESIGNING MANAGEMENT50-60 6 12 6 60-70 10 8 11 70-80 12 7 9 80-90 3 4 3 90-100 3 2 4 Total 34 33 33

02468

101214

50-60 60-70 70-80 80-90 90-100Marks

No.

of s

tude

nts

SCIENCE DESIGNING MANAGEMENT


ANALYZING THE QUESTIONS: Now we will proceed for calculation of data question no 1; SCIENCE STUDENTS:

Marks in mathematics

Mid point “x”

Frequency “f” C.F f x X f x X2

50-60 55 6 6 330 18150 60-70 65 10 16 650 42250 70-80 75 12 28 900 67500 80-90 85 3 31 255 21675

90-100 95 3 34 289 27075 ∑ = 34f ∑ = 2420.xf ∑ = 1766502.xf

Mean =µ =∑∑

fxf .

= 176.71

342420

=

Mean = 176.71=µ Median= =µ~ ).

2( fcn

fh

−+λ

Median = n/2 th term

= 34/2 =17th term

L.C.B=70 f=12 Mid point=75 h=10

)1617(

121070~ −+=µ = 70.8333

Median = 833.70~ =µ Mode= h

fffmffml ×−−

−+ )

2121(

10)31024

1012(70 ×−−

−+= =70.8181

Mode = 8181.70ˆ =µ

STATISTICS SURVEY REPORT 14 Quartile;

Q1 ).4

( fcnfhl −+=

Q1 thn4

= term =34/4=8.5th term

L.C.B = 60 f = 10 C.F = 6 Q1= )65.8(

101060 −+ = 62.5

Standard deviation for sample-grouped data;

)1(

)(1 1

22

−

−=

∑ ∑= =

nn

xfxfns

K

i

K

iiiii

55.11)33(34

)2420(17665034 2

=−×

=s

Standard deviation=11.55 MANAGEMENT STUDENTS: Marks

in mathematics

Mid point “x”

Frequency “f” C.F f x X f x X2

50-60 55 6 6 330 18150 60-70 65 11 17 715 46475 70-80 75 9 26 675 50625 80-90 85 3 29 285 21675

90-100 95 4 33 380 36100 ∑ = 33f ∑ = 2385.xf ∑ = 1830252.xf

Mean =µ =∑∑

fxf .

= 27.72

332385

=

Mean = 27.72=µ

STATISTICS SURVEY REPORT 15 Median= =µ~ ).

2( fcn

fh

−+λ


= 33/2 =16.5th term

L.C.B=60 f=11 C.F=6

Mid point=65 h=10 )65.16(

111060~ −+=µ = 69.54

Median = 54.69~ =µ Mode= h

fffmffml ×−−

−+ )

2121(

10)9622

611(60 ×−−

−+= = 67.142

Mode = 142.67ˆ =µ Quartile;

Q1 ).4

( fcnfhl −+=

Q1 thn4

= term =33/4=8.25th term

L.C.B = 60 f = 11 C.F = 6

Q1= )625.8(111060 −+ = 62.045

Q1 = 62.045 Standard deviation for sample-grouped data;

)1(

)(1 1

22

−

−=

∑ ∑= =

nn

xfxfns

K

i

K

iiiii

24.18)32(33

)2385(18302533 2

=−×

=s

Standard deviation=18.24

STATISTICS SURVEY REPORT 16 DESIGNING STUDENTS:

Marks in mathematics

Mid point “x”

Frequency “f”

C.f f x X f x X2

50-60 55 12 12 660 36300 60-70 65 8 20 520 33800 70-80 75 7 27 525 39375 80-90 85 4 31 340 28900

90-100 95 2 33 190 18050 ∑ = 33f ∑ = 2235.xf ∑ = 156425. 2xf

Mean =µ =∑∑

fxf .

72.6733

2235==

Mean = 72.67=µ Median= =µ~ ).

2( fcn

fh

−+λ


= 33/2 =16.5th term

L.C.B=60 f=8 Mid point=65 h=10 )125.16(

81060~ −+=µ = 65.625

Median = 625.65~ =µ Standard deviation for sample-grouped data;

)1(

)(1 1

22

−

−=

∑ ∑= =

nn

xfxfns

K

i

K

iiiii

56.12)32(33

)2235(15642533 2

=−×

=s

Standard deviation=12.56


Q#2: Is Mathematics Essential For Your Profession?

MALE FEMALE DEPARTMENTS Yes No Yes No

TOTAL

Designing 3 5 5 20 33 Management 16 5 9 3 33 Science 24 7 2 1 34 Total 43 17 16 24 100

01020304050

Yes No Yes No

MALE FEMALE

No

of s

tude

nts

Designing Management Science

COMMENTS: The table shows that the highest number of students who think that mathematics is essential for their professions are science students but students of management and designing departs are also agreed on this point that mathematics have key importance and significant impact on their professions.

STATISTICS SURVEY REPORT 18 Q#3: Do You Like Mathematics?

DEPARTMENTS YES NO TOTAL Designing 14 19 33 Management 28 5 33 Science 26 8 34 Total 68 32 100

0

5

10

15

20

25

30


# O

F ST

UD

ENTS

Series1 Series2

COMMENTS: The comments passed on this question are that the management student’s are much more in the favour to learn mathematics, science students are also in the favour of this course but in less ratio as compare to management students because they think that the course offered hare at our institute don’t influence their professions so they don’t favour to learn it more.

STATISTICS SURVEY REPORT 19 Q#4: What Do You Think About Your Level Of Mathematics?

LEVELS MALE FEMALE TOTAL Average 27 19 46

Good 25 16 41 Excellent 8 5 13

Total 60 40 100

0

5

10

15

20

25

30

MALE FEMALE

Gender

# of

Stu

dent

s

AverageGoodExcellent

We can also drive the probability from the given data, a random sample of 100 students are classified above according to the gender and the level of education. If a person is chosen randomly from this data, the probability would be; A: A person is male and given the person has average level of mathematics. So, P (A) = P (Average Level of Mathematics) = 46/100 P (A ∩ B) = P(Average Level of Maths and Male) = 27/100 So, P (B/A) =

4627

10046/

10027

)()(

==∩AP

BAP

B: Person doesn’t have excellent level of mathematics and given that the person is male. P (A/B) = 52/87

STATISTICS SURVEY REPORT 20 COMMENTS: Here the graphs and the data values indicate the favour to the level of mathematics on the basis of gender, generally the male and female are in average ratio regarding to their interest for mathematics and a very few male and females in our institute have excellent favour ratio for mathematics.


Q#5: Is Mathematics Hard For You? Q#7: Do You Want To Learn More Maths? Departments Hard Not hard Yes No Designing 13 20 14 19 Management 8 25 28 5 Science 5 29 26 8 Total 26 74 68 32

05

101520253035

Hard Not Hard YES NO

No

of s

tude

nts


Q.5 Q.7

COMMENTS: The table shows that the most students who feel maths is not difficult for them but some students of designing feel that maths is hard for them but they want to learn mathematics.

STATISTICS SURVEY REPORT 22 Q#6: Is Your Knowledge In Mathematics Enough For Daily Life Concerned?

DEPARTMENTS YES NO TOTAL Designing 31 2 33 Management 31 2 33 Science 33 1 34 Total 95 5 100

05

101520253035

# of

stu

dent

s

YES NO


COMMENTS: These data comments that the mathematics’ course offered here at TIP provide enough help for their daily life concerned. On the basis of data, students of all the departments agree on the importance of the information provided by these courses.


Q# 8 and 9: You Like Mathematics Due To?

REASONS LIKE DON'T LIKE TOTAL Due to teacher 26 12 38 Due to parent's 5 0 5 Your personal interest 33 4 37 You don't know 4 16 20 Total 68 32 100

0

10

20

30

40

LIKE DON'T LIKEReasons

No

of s

tude

nts

Due to teacher Due to parent'sYour personal interest You don't know

COMMENTS: We can conclude that the majority of students choose to learn mathematics if they have their own personal interest in it and secondly they in to it due to their teacher’s recommendations. Parental interest has a very little effect into it.


Q#10: Regarding Your Ability In Mathematics Can You Provide Help To Some One Else?

GENDER YES NO TOTAL # OF STUDENTS Male 51 9 60

Female 36 4 40 Total 87 13 100

010

20

30

4050

60

YES NO

no o

f stu

dent

s

Male Female

COMMENTS: This question looks upon on the ability of the students good in mathematics and they can provide help to the other students on the basis of their ability in mathematics. In this regard, it is constructive to say that both the males and females in a large ratio encourage helping others in this subject.


CONSOLIDATED DATA:


GRAPH OF CONSOLIDATED DATA:


CONCLUSION: By the comparison of Management, Sciences and Designing faculties, we conclude that all the departments agreed on the intense importance and inimitable significance of Mathematics and think it is essential for all of them, which we think is not expected as our suppositions about Designing department. It is a common fact, students having harder field of study avoid mathematics but here at T.I.P majority of Designing students think that mathematics is hard but on the other hand, majority of them has showed their interests to learn Mathematics and their proportion is slightly higher then the Sciences students. Here it is interesting thing to discuss is that majority of Designing students also thinks that Mathematics is easier as compare to their designing and arts subject, hence on this basis they are interested to learn Mathematics. However, al lot of students in all of the faculties give the response that mathematics is a very interesting and easy subject but at TIP they are not interested to learn it more, may be the reason is that they think it is not compatible to their profession or don’t help them in their profession. Here a very remarkable and significant matter of discussion is that majority of students don’t want to learn the Mathematics on the teaching methods and teaching criteria of their Instructors. Some of the students think that they have good teachers and only on this basis they consider Mathematics interesting and want to learn it while on he other student same ratio of students opposed this object.


RECOMMENDATIONS:

After getting the results of the analysis of our survey we recommend that Mathematics should be taken as “Applied/Associated ” subject in every discipline of textiles.

For the students of the basic classes of textiles, the quality teachers should be provided so that they could develop a good interest in Mathematics in them.

If the parents have low interest in Mathematics and they find it hard to study, then they should keep their views to themselves and should allow their children to choose their field of interest themselves.

There should be a few courses of “Mathematical Modeling”.


REFERENCES:

Introduction To Statistics By: Ronalde Walpole

Applied Mathematics For Business, Economics, And

The Social Sciences By; Frank S. Budnick

Statistics Concepts And Methods

By; S. Khursheed Alam

Elements Of Statistics & Probability By; Shahid Jamal

SOFTWARE USED:

1) Ms Word 2) Ms Excel 3) Ms Equation Editor 3.0 4) Minitab

essentiality of mathematics

Education