Essentiality of mathematics
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Essentiality of mathematics Essentiality of mathematics Document Transcript

  • STATISTICS SURVEY REPORT 2ACKNOWLEDGEMENT: We, Muhammad Imran, Muhammad Aamir Riaz,Muhammad Saeed, worked in a group, to carry out asurvey on “Essentiality Of Mathematics In OurProfessional Life” which is also the requirement of thiscourse, as this survey and the arrangement of data ofthis survey both are very time consuming &overshadowing effort but we thanks Almighty Allahwho empowered us to complete these practical andreport. We would also like to say coordinal thanks andappreciate the memorable behaviour and lovingattitudes of all the students of TIP to whom we havegiven the survey forms and in this regard theircooperation 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 theinstructor of our course, Ma’am Rakshanda Shah for hiscomplete collaboration and assistance. Responsibility for any sort of errors and exclusionsis certainly our.
  • STATISTICS SURVEY REPORT 3TOPIC:“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 ofmathematics for professional field.My report is concerned with the feed back of students about theessentiality and the interest of mathematics in their professional field.The foremost objective is to compare the interest in mathematicsbetween designing, management and textile science and alsocomparison between those students who likes and those who dislikethe mathematics and their marks in exams.QUESTIONNAIRES:Questionnaires can be most simply defined as apprises of collectingsuch 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 ofgathering information from a sample of individuals. This sample isusually just a fraction of the population being studied.
  • STATISTICS SURVEY REPORT 4 Assignment of statisticsEvaluate yourself as a mathematicianName: ________________________Sex: __________________________ class: __________Age: _________________________ year: ___________Discipline: Textile science DesigningManagement1 Your marks in math’s in intermediate Less then 60 60-70 70-80 80-90 Above 902 Is mathematics is essential for your professional field? Yes NO3 Do you like mathematics? Yes NO4 What do you think that what is your level of mathematics? Low High Moderate5 Is mathematics hard for you? YES NO6 Your knowledge in maths is enough for daily life concerned. YES NO7 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 know9 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 know10 Regarding your ability in maths can you provide help to some one else? YES NO Respondent signature:__________
  • STATISTICS SURVEY REPORT 5 “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 descriptiveand inferential. 2 Descriptive statistics 3 Inferential statisticsDESCRIPTIVE STATISTICS:It deals with the collections classifications summarization andpresentation of data.INFERENTIAL STATISTICS:It deals with the conclusions drawn about a population using the dataof a sample taken from the same population.POPULATION:Population consists of the totality of the observations with which weare 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 chosenin such a way that very subset of n observations of the population hasthe same probability of being selected.PROBABILITY:A probability is a numeric measure of the likelihood or chance that aparticular event will occur.Symbolically it is written as;
  • STATISTICS SURVEY REPORT 6 n( A) P( A) = n(S )It is further distributed into following ones;1. Binomial 2. Poisson3. Hyper geometric 4. NormalMEASUREMENT OF TENDENCY:Generally we have two types of tendencies; 1. Measures of central tendency 2. Measures of dispersion1. MEASURES OF CENTRAL TENDENCY:It is defined as a single value of the data, which truly represents thewhole data.It is further classified into; i. Arithmetic Mean ii. Geometric Mean iii. Harmonic Mean iv. Median v. ModeARITHMETIC MEAN:It is the most commonly used measure and usually termed as simplemean. “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 andis denoted by x . n ∑x i x= i =1 nWhereas, if the data is not a sample but the entire population of Nvalues, it is termed as population mean and is denoted by µ. N ∑x i µ= i =1 NWEIGHTED ARITHMETIC MEAN:The mean of a data gives equal importance or weights to each of thevalues of raw data. In some general cases all values in the raw data
  • STATISTICS SURVEY REPORT 7don’t have the same importance. A weighted mean is used to assignany degree of importance to each value of the data by choosingappropriate weights for these values. xw = ∑ w.x ∑wHere, “w” are the weights assigned to the values of data.GEOMETRIC MEAN:Geometric mean is defined only for non-zero positive values. It is thenth root of the product of n values in the data. G = n x1 x2...xKWEIGHTED GEOMETRIC MEAN;If weights are assigned to the values of the data, in this regard we cancalculate the geometric mean. G.M . = Anti log[ ∑ w.log x ] ∑wHARMONIC MEAN:Harmonic mean is defined only for non-zero positive values; it is thereciprocal of mean of reciprocal of values. K H = K 1 ∑i = 1 xiWEIGHTED HARMONIC MEAN:If all values of the data are not equally important, a weightedharmonic mean is calculated after assigning appropriate weights tothe values of the data. H .M . = ∑w w ∑( x )MEDIAN:Median is defined as the middle value of the data when the values arearranged in ascending or descending order. ~ µ=λ+ h ( n − c. f ) f 2
  • STATISTICS SURVEY REPORT 8MEDIAN OF A FREQUENCY DISTRIBUTION:Values of the data in an interval are evenly or uniformly spread inthat interval is known as the median of the frequency distribution. Width of the interval No. of values in the intervalPARTITION VALUES OR QUARTILES:QUARTILES:There are three values, which can divide the arranged data in fourequal parts or quarters. These values are called quartiles. h n Qi = l + ( i − c. f ) f 4DECILES:There are nine values, which can divide the arranged data in ten equalparts. h n Di = l + ( i − c. f ) f 10PERCENTILES:Similarly, the 99 values, which divide the arranged data in 100 equalparts, are called percentiles. h n Pi = l + ( i − c. f ) f 100MODE:Mode is a measure of central tendency generally used when the data isof 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 maximumnumber of times in the data. fm − f 1 Mode = x = l + ( ˆ )×h 2 fm − f 1 − f 2MODE OF A FREQUENCY DISTRIBUTION:In a frequency distribution mode is that value of the variable forwhich the frequency curve takes maximum height.
  • STATISTICS SURVEY REPORT 9A frequency distribution with one mode is called unimodal and withtwo modes is called a bimodal frequency distribution.2. MEASURES OF DISPERSION:The dispersion is defined as the scatter or spread of the values fromone another or from some common values. The method to compute theamount of dispersion present in any data is called “Measures ofDispersion” or “Measures of Variation”.The measures of dispersion are further classified into; i. Range ii. Quartile Deviation iii. Mean Deviation iv. Standard DeviationRANGE:Range is the simple measure of dispersion and is defined as thedifferences between the maximum and minimum values of the data. R = Xmax− XminRange is generally rough and crude measurement as it ignores thevariation among all the values.QUARTILE DEVIATION:The difference between the third and first quartiles is called theinterquartile range and quartile deviation is the half of theinterquartile range and is also known as the semi-interquartile range. Q3 − Q1 Q.D. = 2MEAN DEVIATION:Dispersion can be measured in terms of the quantities that each valueof the data deviates from average value.Mean deviation for ungrouped data; M .D. = ∑| x − x | nMean deviation for grouped data; K ∑f i | xi − x | M .D . = i =1 K ∑f i =1 i
  • STATISTICS SURVEY REPORT 10Hence in this regard it is defined as, sum of absolute deviations frommean divided by the number of values.STANDARD DEVIATION:Standard Deviation is the most widely used measure of dispersion andis 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 −1Standard deviation for population-ungrouped data; N ∑(x − µ) i 2 σ = i =1 NStandard 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
  • STATISTICS SURVEY REPORT 11SAMPLING OF THE DATA: POPULATION SAMPLEDEPARTMENT TOTAL TOTAL M F M FDesigning 12 39 51 8 25 33Management 38 14 52 21 12 33Science 130 3 133 31 2 34Total 180 56 236 60 40 100Here at TIP, after conducting this survey, we analyzethat male in Science department are more proficientof learning Mathematics while in the Designingdepartment female-heads are more engrossed andinterested to learn mathematics as compare to themales.
  • STATISTICS SURVEY REPORT 12Q#1: Your Marks In Mathematics In Intermediate?GENERAL DATA:This data is regarding to all the departments and onthe ratio of the marks which the students got duringtheir 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 12No. of students 10 8 6 4 2 0 50-60 60-70 70-80 80-90 90-100 Marks
  • STATISTICS SURVEY REPORT 13ANALYZING THE QUESTIONS:Now we will proceed for calculation of data question no 1;SCIENCE STUDENTS: Marks in Mid Frequencymathematics 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 = 176650Mean = µ = ∑ f .x ∑f 2420 = = 71.176 34Mean = µ = 71.176 ~ h nMedian= µ = λ + ( − c. f ) f 2Median = 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 1Mode= l + ( )×h 2 fm − f 1 − f 2 12 − 10 = 70 + ( ) × 10 =70.8181 24 − 10 − 3Mode = µ = 70.8181 ˆ
  • STATISTICS SURVEY REPORT 14Quartile; 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 10Q1= 60 + (8.5 − 6) = 62.5 10Standard deviation for sample-grouped data; K K n∑ f x − (∑ fi xi )2 2 i i s= i =1 i =1 n(n −1) 34 × 176650 − (2420) 2s= = 11.55 34(33)Standard deviation=11.55MANAGEMENT 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 = 183025Mean = µ = ∑ f .x ∑f 2385 = = 72.27 33Mean = µ = 72.27
  • STATISTICS SURVEY REPORT 15 ~ h nMedian= µ = λ + ( − c. f ) f 2Median = n/2 th term = 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 1Mode= l + ( )×h 2 fm − f 1 − f 2 11 − 6 = 60 + ( ) × 10 = 67.142 22 − 6 − 9Mode = µ = 67.142 ˆQuartile; 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 10Q1= 60 + (8.25 − 6) = 62.045 11 Q1 = 62.045Standard deviation for sample-grouped data; K K n∑ f x − (∑ fi xi )2 2 i i s= i =1 i =1 n(n −1) 33 × 183025 − (2385) 2s= = 18.24 33(32)Standard deviation=18.24
  • STATISTICS SURVEY REPORT 16DESIGNING STUDENTS: Marks in Mid Frequency C.f fxX f x X2mathematics 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 = 156425Mean = µ = ∑ f .x ∑f 2235 = = 67.72 33Mean = µ = 67.72 ~ h nMedian= µ = λ + ( − c. f ) f 2Median = n/2 th term = 33/2 =16.5th termL.C.B=60 f=8Mid point=65 h=10 ~ 10 µ = 60 + (16.5 − 12) = 65.625 8 ~Median = µ = 65.625Standard deviation for sample-grouped data; 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)Standard deviation=12.56
  • STATISTICS SURVEY REPORT 17Q#2: Is Mathematics Essential For Your Profession? DEPARTMENTS MALE FEMALE TOTAL Yes No Yes NoDesigning 3 5 5 20 33Management 16 5 9 3 33Science 24 7 2 1 34Total 43 17 16 24 100 Designing Management Science 50 No of students 40 30 20 10 0 Yes No Yes No MALE FEMALECOMMENTS:The table shows that the highest number of students who think thatmathematics is essential for their professions are science students butstudents of management and designing departs are also agreed on thispoint that mathematics have key importance and significant impact ontheir professions.
  • STATISTICS SURVEY REPORT 18Q#3: Do You Like Mathematics? DEPARTMENTS YES NO TOTALDesigning 14 19 33Management 28 5 33Science 26 8 34Total 68 32 100 Series1 Series2 30 25 # OF STUDENTS 20 15 10 5 0 Designing Management ScienceCOMMENTS:The comments passed on this question are that the managementstudent’s are much more in the favour to learn mathematics, sciencestudents are also in the favour of this course but in less ratio ascompare to management students because they think that the courseoffered hare at our institute don’t influence their professions so theydon’t favour to learn it more.
  • STATISTICS SURVEY REPORT 19Q#4: What Do You Think About Your Level OfMathematics? 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 GenderWe can also drive the probability from the given data, a randomsample of 100 students are classified above according to the genderand the level of education.If a person is chosen randomly from this data, the probability wouldbe;A: A person is male and given the person has average level ofmathematics.So, P (A) = P (Average Level of Mathematics) = 46/100P (A ∩ B) = P(Average Level of Maths and Male) = 27/100 P( A ∩ B) 27 46 27So, P (B/A) = = / = P( A) 100 100 46B: Person doesn’t have excellent level of mathematics and given thatthe person is male.P (A/B) = 52/87
  • STATISTICS SURVEY REPORT 20COMMENTS:Here the graphs and the data values indicate the favour to the level ofmathematics on the basis of gender, generally the male and female arein average ratio regarding to their interest for mathematics and a veryfew male and females in our institute have excellent favour ratio formathematics.
  • STATISTICS SURVEY REPORT 21Q#5: Is Mathematics Hard For You?Q#7: Do You Want To Learn More Maths?Departments Hard Not hard Yes NoDesigning 13 20 14 19Management 8 25 28 5Science 5 29 26 8Total 26 74 68 32 Designing Management Science 35 30 No of students 25 20 15 10 5 0 Hard Not Hard YES NO Q.5 Q.7COMMENTS:The table shows that the most students who feel maths is not difficultfor them but some students of designing feel that maths is hard forthem but they want to learn mathematics.
  • STATISTICS SURVEY REPORT 22Q#6: Is Your Knowledge In Mathematics Enough ForDaily Life Concerned? DEPARTMENTS YES NO TOTAL Designing 31 2 33 Management 31 2 33 Science 33 1 34 Total 95 5 100 Designing Management Science 35 30 # of students 25 20 15 10 5 0 YES NOCOMMENTS:These data comments that the mathematics’ course offered here atTIP provide enough help for their daily life concerned. On the basis ofdata, students of all the departments agree on the importance of theinformation provided by these courses.
  • STATISTICS SURVEY REPORT 23Q# 8 and 9: You Like Mathematics Due To? REASONS LIKE DONT LIKE TOTALDue to teacher 26 12 38Due to parents 5 0 5Your personal interest 33 4 37You dont know 4 16 20Total 68 32 100 Due to teacher Due to parents Your personal interest You dont know 40 No of students 30 20 10 0 LIKE Reasons DONT LIKECOMMENTS:We can conclude that the majority of students choose to learnmathematics if they have their own personal interest in it and secondlythey in to it due to their teacher’s recommendations. Parental interesthas a very little effect into it.
  • STATISTICS SURVEY REPORT 24Q#10: Regarding Your Ability In Mathematics Can YouProvide 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 NOCOMMENTS:This question looks upon on the ability of the students good inmathematics and they can provide help to the other students on thebasis of their ability in mathematics. In this regard, it is constructiveto say that both the males and females in a large ratio encouragehelping others in this subject.
  • STATISTICS SURVEY REPORT 27CONCLUSION:By the comparison of Management, Sciences and Designingfaculties, we conclude that all the departments agreed onthe intense importance and inimitable significance ofMathematics and think it is essential for all of them, whichwe think is not expected as our suppositions about Designingdepartment. It is a common fact, students having harder field of studyavoid mathematics but here at T.I.P majority of Designingstudents think that mathematics is hard but on the otherhand, majority of them has showed their interests to learnMathematics and their proportion is slightly higher then theSciences students. Here it is interesting thing to discuss isthat majority of Designing students also thinks thatMathematics is easier as compare to their designing and artssubject, hence on this basis they are interested to learnMathematics. However, al lot of students in all of thefaculties give the response that mathematics is a veryinteresting and easy subject but at TIP they are notinterested to learn it more, may be the reason is that theythink it is not compatible to their profession or don’t helpthem in their profession.Here a very remarkable and significant matter of discussionis that majority of students don’t want to learn theMathematics on the teaching methods and teaching criteriaof their Instructors. Some of the students think that theyhave good teachers and only on this basis they considerMathematics interesting and want to learn it while on heother student same ratio of students opposed this object.
  • STATISTICS SURVEY REPORT 28RECOMMENDATIONS: 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”.
  • STATISTICS SURVEY REPORT 29REFERENCES: 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