Introduction to business Statistics.

MIHE:INSTRACTOr:BILAL KHANMBA(MARKETING)Msc(Economics)

Chapter No 01Introduction to business Statistics.What is statistics?Numerical data relating to an aggregate of individuals, the science of collecting, analyzing and interpreting data is called statistics.Conti

Height(ft)Weights(kg)No. of students4.245-4914.550-5444.755-5917660-64285.565-6925570-74185.875-7913Importance of statistics in Business.Statistics play an important role in business, because provides a quantitative basis for arriving at decisions in all matters connected with operating of business.For example producers must know the demand of his consumers.Statistics would help to plan production according to the demands of consumersContiThe banks make use of statistics while framing their policies. The banks have to conduct constant enquiries regularly deposits under different categories, the nature of demand for daily with-drawls etc.Difference between Parameter and statistic.Parameter. A number that describes some property of a population is called parameter For example a numerical value such as mean and mode etc..ContiStatistic. A number that describes some property of a sample is called statistic.For example the average length calculated for a random(hit and miss) sample of a college students.Difference between population and sample.Population. The aggregate or totality of all the individual items about which information is required is called populationFor example if 1000 students in the college that we classified according to blood type.Conti.Sampling. The study of observing the single part or only a part of the population , such a part is called sampling.Difference between Descriptive and inferential statistics.Descriptive statistics. Those statistics method which is concerned with collecting and describing a set of data so as to yield meaningful information.For example teacher computes an average grade for his statistics class. The average grade describes the performance of that particular class. Coati..Inferential statistics. Those statistics methods which is concerned with the analyzing of a subset of a data leading to inference about the entire set of a data. For example the academic records of the metric classes during the past five years at a nearby government school show that 45% of the entering freshmen eventually matriculated.What is variable.A quantity which may take any one of a specified set of values.For example the height of a students, rainfall at a place, price of a commodity etc.Discrete Variable.A discrete variable can assume only a finite number.For example the number of children in a family, the number of goals scored by a player etc.Continuous variableA continuous variable may take an infinite number of values between any two points such as the height of a student, the temperature at a place etc. Quantitative variable.If the values are expressed numerically the variable is said to be quantitative.Foe example age, weight, income, number of children etc.Qualitative variable.If the values are not expressed in the numerical form is called qualitative variable.For example smoking, poverty intelligence etc.Chapter no 2Collection and Presentation Of data. What do you mean by classification.Classification. It is the process of arranging data into sequences and groups according to their common characteristics.For example we may arrange the marks into group of 60 marks each like 01 to 59, 60 t0 119 etc.Conti..Weights(kg) No. of students45-49150-54455-591760-642865-692570-741875-7913Types of classification:1: Descriptive 2:Numerical.Descriptive classification:When the data are classified on the basis of quality which are incapable of quantitative measurement the classification is said to be descriptive.For example classification according to the sex and marital status divide the population into six classes.Male marriedMale unmarried Male widowed Female married Female unmarried Female widowedNumerical ClassificationThis type of classification is applicable to quantitative data only.For example data related to the height, weight, income and production etc.

What do you mean by tabulation of statistical dataTabulation simply means presenting of data through tables.It is the next of classification in the process of statistical investigation.To be more precise tabulation is an orderly arrangement of data into columns and rows.Conti.ClassesClass boundaries'Mid pointsTallyFrequency65-8464.5-84.574.5//// ////985-10484.5-104.594.5//// //// 10105-124104.5-124.5114.5//// //// //// //17125-144124.5-144.5134.5//// ////10145-164144.5-164.5154.5////5165-184164.5-184.5174.5////4185-204184.5-205.5194.5////5Simple tabulationA simple tabulation contains data regarding one characteristics only.Information relating to the other characteristics being ignored. ContiWeights(kg) No. of students45-49150-54455-591760-642865-692570-741875-7913Complex tabulationShows the division of the data into two or more categories:

Height(ft)Weights(kg)No. of students4.245-4914.550-5444.755-5917660-64285.565-6925570-74185.875-7913DistributionArrangement of data according to the values of a variable characteristics is called distribution Years1998 1999 2000 2001 2002Population(In Millions) 40 45 60 64 68ContiYearImportsexports1992-1993841993-19941061994-19951291995-199618131996-19972017What is frequency distribution?A large mass of data possessing different characteristics is grouped into different classes.The observation are determined in each class.The arrangement of these classes into tabular form makes frequency distribution.

Conti..Class limitTallyFrequencyClass boundaries48.6-53.5/148.55-53.5553.6-58.5//253.55-58.5558.6-63.5/158.55-63.5563.6-68.5////463.55-68.5568.6-73.5//// ///868.55-73.5573.6-78.5//// 573.55-78.5578.6-83.5//// ///878.55-83.5583.6-88.5/183.55-88.5588.6-93.5/188.55-93.5593.6-98.5/193.55-98.5532Class frequency and grouped dataThe number of observation falling in a class makes a class frequency.Data organized and summarized in the form of frequency distribution are called grouped data.Main points of preparing a frequency distributionNumber classes and their lengthsClass-LimitClass boundariesClass-Marks or Mid pointClass frequencyNumber of classes and their lengthsA frequency distribution should not have too few or too many large.Depending upon a particular data.The number of classes should not exceed 25 and should not be less than 6.Class LimitThe limit of the class should be so fixed that the mid point of each class interval fall on an integer and not a fractionClass boundaries

If one have grouped frequency distribution with class limit having a gap between the upper class limit of one class and the lower class limit of the next classClass-Marks or Mid pointFormula : lower class + upper class 2Class frequencyThe frequency of a class interval is the total number of items falling in that class interval Also called class tally sheetUsually after every four lines in a class the fifth item is marked by horizontal or slanted lines across the strokesQ : make a group frequency distribution from the following data .106 107 76 82 109 107 115 93 95 123 125 111 92 86 70 126 68 130 129 139 119 115 128 100 186 84 99 113 204 111 141 136 123 90 115 98 110 78 185 162 178 140 112 173 146 158 194 148 90 107 181 131 75 184 104 110 80 118 82.By scanning the data we find that the largest weight is 204 and the lowest is 68 so the range is 204-68=136Decide on the number of classes into which the data are to be grouped we used H.A Sturges rule.K= 1+3.3logN.Where k denotes the number of classes and N is the total number of observation.Conti.Frequency distribution.

ClassesClass boundaries'Mid pointsTallyFrequency65-8464.5-84.574.5//// ////985-10484.5-104.594.5//// //// 10105-124104.5-124.5114.5//// //// //// //17125-144124.5-144.5134.5//// ////10145-164144.5-164.5154.5////5165-184164.5-184.5174.5////4185-204184.5-205.5194.5////5Q: arrange the data given below in an array and construct a frequency distribution using a class interval of 5 indicate the class boundaries and class limit clearly79.4, 71.6, 95.5, 73, 74.2, 81.8, 90.6, 55.9, 75.2, 81.9, 68.9, 74.2, 80.7, 65.7, 67.6, 82.9, 88.1, 77.8, 69.4, 83.2, 82.7, 73.8, 64.2, 63.9, 58.3, 48.6, 83.5, 70.8, 72.1, 71.9, 59.4, 77.6Ans: the value of variate range from 48.6 to 95.5. we take class interval of length 5.No. of classes = range class interval 95.5 48.6 = 9.38 = 10 5 Cont.Class limitTallyFrequencyClass boundaries48.6-53.5/148.55-53.5553.6-58.5//253.55-58.5558.6-63.5/158.55-63.5563.6-68.5////463.55-68.5568.6-73.5//// ///868.55-73.5573.6-78.5//// 573.55-78.5578.6-83.5//// ///878.55-83.5583.6-88.5/183.55-88.5588.6-93.5/188.55-93.5593.6-98.5/193.55-98.5532What is simple bar chart:The simple bar chart is particularly appropriate for a linear or one dimension comparison. The scale for construction of simple bar chart should be such as facilitates the representation of largest bar quite conveniently. Conti.Years1998 1999 2000 2001 2002Population(In Millions) 40 45 60 64 68Chart. 80604020019981999200020012002Multiple bar chartIn this type of chart we represent two or more than two sets of a data in one chart than more than one chart is used.This can be explained with the help of example, the following table give the imports and exports of Pakistan for year 1992 to1997.Conti..YearImportsexports1992-1993841993-19941061994-19951291995-199618131996-19972017Chart.Subdivided bar charts.Subdivided bar are used to present such data which are to be shown in parts, or which are the totals of various subdivisions. The components parts are shaded or colored differently so as to distinguish different parts ContiFor example if we want to present the development in the field of industry, transports, and agricultural for Pakistan , we will draw bars with lengths proportional to the total populations.Conti.YearsIndus2001try TransportsagriculturalTotal19981008040220199912010050270200013012055305Chart..Pie charts.The reason for the popularity of pie chart is the easiness and convenience in its constructions. It is also known as a circle chart. The procedure is very simple take the total of these quantities equal to an angle of 360 degree and than convert the quantities in terms of angles using the following formula. angle = Quantity X 360 TotalConti.This can be explained with the help of example which is clear from the following table that shows the population of provinces. NamePopulation in millionsKabul26Jalalabad23wardak8Qandahar4Helmand65Conti.The corresponding angles needed to draw the the chart are given below. NamesPopulation in millionsAngles of sectorKabul2626/126x360=74.3Jalalabad2323/126x360=65.7Wardak88/126x360=23Qandahar44/126x360=11Helmend6565/126x360=126Chart.HelmandHistogram.When the class-boundaries are marked along the x-axis and rectangle are constructed width proportional to class interval size and heights proportional to class frequencies. The resulting graph will be called a histogram.Continue..Class limits40-4950-5964540-6970-7980-8990-99100-109Frequency1345421Chart. 4321039.5549.559.569.579.589.599.5109.5Class BoundriesFrequency61Frequency PolygonA frequency polygon is the geometric shape obtained by connecting with straight lines .The mid point of adjacent intervals of a histogram. Following figure shows the frequency polygon .Continue:Class limits40-4950-5960-6970-7980-8990-99100-109Class marks44.554.564.574.584.594.5104.5Frequency1345421Chart:

chapter No 03

\Measures of central tendency or averages:Central Tendency:The tendency of observation to cluster in the central part of the data set is called central tendency.As central tendency indicates the location or general position of the data in the observation is called measure of location or position.Location are generally known as Averages. Types of Averages:The most common types of averages are:(1) The arithmetic Mean.(2) The Geometric Mean.(3) The Harmonic Mean. (4) The Median. (5) The Mode.Arithmetic Mean:It is defined as the value obtained by dividing the sum of all the observations by their number. Mean = Sum of all observations

Number of observations Population Mean:If the given set of observations represents a population than the mean is called as population mean, which is usually represented by u(mu) .Sample mean:If the given set of observations represents a sample, than the mean is called as sample mean.Sample mean is represented by x by putting a bar over it.Q:The marks obtained by 9 students are given below calculate the arithmetic mean.45,32,37,46,39,36,41,48,36.The mean is given by.

X = 45+32+37+46+39+36+41+48+36

09 X = 360 =40 marks. 09Q= The mean heights and the number of students in three sections of a statistics class are given below.SectionNumber of boysMean heightA4062B3758C4361Conti.Find the overall mean height of 120 boys:n1=40, n2=37, n3= 43 andX1 = 62, X2 = 58,X3 = 61

X = n1X2+n2X2+n3X3 n1+n2+n3 Conti (40x62) +(37x58) +(43x61)

40 + 37 + 43 7249 = 60.4 Ans

120Mean from group data:When the data is very large the data are organized into a frequency distribution.Formula:

X = f1X1 + f2X2 + fkXk

f1 + f2 + .fk