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;

n( A)
P( A) =
n(S )
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

∑x i
x= i =1

n
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

∑x i
µ= i =1

N

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

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.
xw =
∑ w.x
∑w
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.

G = n x1 x2...xK

WEIGHTED GEOMETRIC MEAN;
If weights are assigned to the values of the data, in this regard we can
calculate the geometric mean.
G.M . = Anti log[
∑ w.log x ]
∑w
HARMONIC MEAN:
Harmonic mean is defined only for non-zero positive values; it is the
reciprocal of mean of reciprocal of values.
K
H = K
1
∑i = 1 xi

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.
H .M . =
∑w
w
∑( x )
MEDIAN:
Median is defined as the middle value of the data when the values are
arranged in ascending or descending order.
~
µ=λ+ h ( n − c. f )
f 2


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.

Width of the interval
No. of values in the interval

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.

h n
Qi = l + ( i − c. f )
f 4
DECILES:
There are nine values, which can divide the arranged data in ten equal
parts.
h n
Di = l + ( i − c. f )
f 10
PERCENTILES:
Similarly, the 99 values, which divide the arranged data in 100 equal
parts, are called percentiles.
h n
Pi = l + ( i − c. f )
f 100
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.
fm − f 1
Mode = x = l + (
ˆ )×h
2 fm − f 1 − f 2

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

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.
R = Xmax− Xmin
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.
Q3 − Q1
Q.D. =
2

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;
M .D. =
∑| x − x |
n
Mean deviation for grouped data;
K

∑f i | xi − x |
M .D . = i =1
K

∑f
i =1
i

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;
n

∑ (x − x)i
2

s= i =1

n −1
Standard deviation for population-ungrouped data;
N

∑(x − µ) i
2

σ = i =1

N
Standard deviation for sample-grouped data;
K K
n∑ f x − (∑ fi xi )2 2
i i
s= i =1 i =1

n(n −1)
Standard deviation for population-grouped data;
K K
N∑ f x − (∑ fi xi )2 2
i i
σ= i =1 i =1

N


SAMPLING OF THE DATA:

POPULATION SAMPLE
DEPARTMENT TOTAL TOTAL

M F M F

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 MANAGEMENT
50-60 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

SCIENCE DESIGNING MANAGEMENT

14
12
No. of students

10
8
6
4
2
0
50-60 60-70 70-80 80-90 90-100
Marks


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

SCIENCE STUDENTS:

Marks in Mid Frequency
mathematics point “f” C.F fxX f x X2
“x”
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
∑f = 34 ∑ f .x = 2420 ∑ f .x2 = 176650

Mean = µ = ∑
f .x
∑f
2420
= = 71.176
34
Mean = µ = 71.176

~ h n
Median= µ = λ + ( − c. f )
f 2

Median = n/2 th term
= 34/2
=17th term
L.C.B=70 f=12
Mid point=75 h=10

~ 10
µ = 70 + (17 − 16) = 70.8333
12
~
Median = µ = 70.833

fm − f 1
Mode= l + ( )×h
2 fm − f 1 − f 2
12 − 10
= 70 + ( ) × 10 =70.8181
24 − 10 − 3
Mode = µ = 70.8181
ˆ


Quartile;
Q1 = l + h ( n − c. f )
f 4
Q1 = n th term =34/4=8.5th term
4
L.C.B = 60 f = 10 C.F = 6
10
Q1= 60 + (8.5 − 6) = 62.5
10

K K
n∑ f x − (∑ fi xi )2
2
i i
s= i =1 i =1

n(n −1)

34 × 176650 − (2420) 2
s= = 11.55
34(33)

Standard deviation=11.55

MANAGEMENT STUDENTS:

Marks Mid
Frequency
in point C.F fxX f x X2
“f”
mathematics “x”
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
∑f = 33 ∑ f .x = 2385 ∑ f .x2 = 183025

Mean = µ = ∑
f .x
∑f
2385
= = 72.27
33
Mean = µ = 72.27


~ h n
Median= µ = λ + ( − c. f )
f 2

= 33/2
=16.5th term

L.C.B=60 f=11 C.F=6
Mid point=65 h=10

~ 10
µ = 60 +(16.5 − 6) = 69.54
11
~
Median = µ = 69.54

fm − f 1
Mode= l + ( )×h
2 fm − f 1 − f 2
11 − 6
= 60 + ( ) × 10 = 67.142
22 − 6 − 9
Mode = µ = 67.142
ˆ

Quartile;
Q1 = l + h ( n − c. f )
f 4
n term =33/4=8.25th term
Q1 = th
4

L.C.B = 60 f = 11 C.F = 6
10
Q1= 60 + (8.25 − 6) = 62.045
11
Q1 = 62.045

K K
n∑ f x − (∑ fi xi )2
2
i i
s= i =1 i =1

n(n −1)

33 × 183025 − (2385) 2
s= = 18.24
33(32)


DESIGNING STUDENTS:

Marks in Mid Frequency C.f fxX f x X2
mathematics point “f”
“x”
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
∑f = 33 ∑ f .x = 2235 ∑ f .x 2
= 156425

Mean = µ = ∑
f .x
∑f
2235
= = 67.72
33
Mean = µ = 67.72

~ h n
Median= µ = λ + ( − c. f )
f 2

= 33/2
=16.5th term
L.C.B=60 f=8
Mid point=65 h=10

~ 10
µ = 60 + (16.5 − 12) = 65.625
8
~
Median = µ = 65.625

K K
n∑ f x − (∑ fi xi )2
2
i i
s= i =1 i =1

n(n −1)
33 × 156425 − (2235) 2
s= = 12.56
33(32)


Q#2: Is Mathematics Essential For Your Profession?

DEPARTMENTS MALE FEMALE TOTAL
Yes No Yes No
Designing 3 5 5 20 33
Management 16 5 9 3 33
Science 24 7 2 1 34
Total 43 17 16 24 100

Designing Management Science

50
No of students

40
30
20
10
0
Yes No Yes No
MALE FEMALE

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.


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

Series1 Series2

30

25
# OF STUDENTS

20

15

10

5

0

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.


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

30

25
# of Students

20
Average
15 Good
Excellent
10
5

0
MALE FEMALE
Gender

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
P( A ∩ B) 27 46 27
So, P (B/A) = = / =
P( A) 100 100 46
B: Person doesn’t have excellent level of mathematics and given that
the person is male.
P (A/B) = 52/87


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

35
30
No of students

25
20
15
10
5
0
Hard Not Hard YES NO
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.


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


35
30
# of students

25
20
15
10
5
0
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

Due to teacher Due to parent's
Your personal interest You don't know
40
No of students

30
20
10
0
LIKE Reasons DON'T LIKE

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

Male Female

60
50
no of students

40
30
20
10
0
YES NO

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

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