Statistical Methods for Economics: Data Classification and Frequency Distribution

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[Music] [Music] hello Learners welcome to the course

statistical methods for economics module 2 in this session we will discuss the concepts related to classify the data

for further statistical analysis presenting the data in the form of table preparation of the univariate frequency

distribution table preparation of the bivariate frequency distribution table concept of marginal and conditional

distribution in module 1 we had discussed about the terms associated with Statistics importance of Statistics

in economics how the data is collected also the differences between sensors and sampling in this module we shall discuss

about how the data that we have collected is to be classified and presented the raw data are so vinous and

huge that they are unwi and incomprehensible so having collected and edited the data

the next important step is to present it in a readily comprehensible form which will highlight the important

characteristic of the data facilitate comparisons and render it suitable for processing and

interpretation this can be done by classifying and tabulating the data properly we shall now look into certain

objectives of classification classification helps to transform unstructured data into structured data

classification to present the complex data into a simple form classification points forth the similarities and

differences between the items classification brings in uniformity among the facts classification

facilitates for comparative study between the two items classification helps to establish

relationship between the two series classification helps to present the data in a condensed

form we shall now look into the functions of classification classification helps in

presenting the raw data in a concise and simple form that it condenses the data classification facilitate

comparison by dividing the raw data on the basis of their similarities and resemblances classification helps to

study the relationships classification provides basis for tabulation and Analysis of

data classification enables us to identify the possible characteristics in the

data the following rules are to be followed while class classifying the data classification should be

unambiguous classification should be exhaustive and mutually exclusive classification should be

stable classification should be suitable for the purpose classification should be

flexible the different types of classification are simple classification if only two attributes

are at the base then such a classification is called as simple classification for example gender can be

classified as male and female manifold classification if more than two

attributes are there at the base then such a classification is called as manifold

classification for example the data of a population can be classif ified as male and female further the gender can be

classified according to their marital status as married and unmarried which is further classified as literate and

illiterates the following are the basis of classification geographical

classification in geographical classification data are classified on the basis of places or geographical

locations for example the data of certain District which can be classified taluk wise chronological classification

when the data are classified on the basis of time then it is known as chronological

classification series of data arranged with respect to time is known as time series for example the data related to

Import and Export for the past 10 years qualitative classification if the data is classified

on the basis of non-measurable characteristic then such a classification is called as qualitative

classification for example the classification of the data based on religion gender type of

business quantitative classification if the data is classified on the basis of the measurable characteristic then such

a classification is called as quantitative classification for example the classification of the data based on

age annual income of a family family size Etc

tabulation once the data is classified presenting it in a logical way in vertical columns and horizontal rows of

numbers with sufficient explanation and qualifying words in the form of titles headings and notes to fully understand

the facts and their origin can be done by tabulating them however in terms of Professor bow tabulation is defined as

the intermediate process between the accumulation of data in whatever form they are obtained and the final reasoned

account of the result shown by the statistics while constructing the table certain

pattern is to be adopted that can be done easily by constructing the table in Parts every table has to have a table

number a book or article may contain more than one table hence for the proper identification and easy referencing the

tables should be numbered in logical sequence every table must be given a suitable title the title is usually

placed on the top of the table followed by the title a head note is given below the title is a prominent type usually

centered and enclosed in brackets for further description of the content of the table headnote is also referred as

Preparatory note the roow head headings of the table are called as stops and the column

headings of the table are called as captions the numerical information placed in the table is referred to as

body of the table when a feature of the table has not been completely explained and it

further needs explanation or some additional information is provided as foot note this foot note may be related

to the title captions stubs or anything related to the table they are identified with the symbols like Aster double Aster

at sign dagger Etc if any secondary data are used then it is mentioned in the source note The

Source note should give the name of the journal or periodical along with the public ation date its volume number page

number Etc so anyone who uses the data might verify the accuracy of the figures used in the table with that of the

original source of information this is the blank layout of the

table let us now look into certain points that need to be kept in mind while constructing the table firstly the

table should be constructed according to the paper size with more rows than columns a logical order such as

alphabetical chronological geographical so on should be followed with the information that are to be arranged in

the steps and captions the table should not be overloaded it should be complete and

self-explanatory the cells of the table should not left blank either put a dash or WR na which indicates not applicable

in the blank CS of the table also it is not appropriate to use dto marks in the

table now let us look into the various types of tables the tabular representation of

only one characteristic is termed as oneway tabulation the tabular representation of

two characteristics is termed as two-way tabulation if more than two characteristics are represented in a

table it is called manifold table in manifold tabulation steps and captions can be broken down into subc captions

and substeps frequency distribution the data pertaining to

quantitative characteristic can be organized as individual observations discrete or ungroup

frequency distribution continuous frequency distribution or grouped frequency

distribution we shall now look into the terminologies associated with frequency distribution with an

example the data was collected from 20 homes from a village of mysuru regarding how many bikes the own and the responses

were as follows 2 3 0 2 1 0 2 2 3 2 5 1 2 2 1 5 0 3 4 1 the data which are recorded as

collected is called as raw data and it is in the basic form this is also called as individual

observations now we see that certain observations are repeated the number of times each value in the variable occurs

is called as frequency if these values are represented according to their magnitude

in the form of the table it is called as frequency distribution the process of counting of

the frequencies are done by small vertical bars scored parallel to each other and put opposite to a particular

value these are called as tally bars usually a block of five bars are used for counting

process now above example let us construct a frequency distribution denote the variable as

number of bikes as X observe that in the data the minimum value is zero and maximum value is 5

hence X can take the values 0 to 5 now let us count them using tally bars the first observation is two so place a

tally mark next to two the next observation is three so place a tally mark next to three then 0 2 1 0 2 2 3 so

now 2 is repeating for the fifth time so let us put a diagonal line on the four vertical bars this helps in Easy

counting after grouping all the values we count the tally bars and write the frequencies if the values of the

variables are discontinuous and the frequency distribution is done for them then such series is called as

ungrouped series let us consider the following example the manager of Bilo

supermarket in Mount Pleasant Road Island gather the following information on the number of times a customer visits

the store during a month and the responses of 50 customers are as follows starting with zero as the lower

limit of the class and using class interval of three organize the data into frequency

distribution so we shall construct the class interval starting with zero and the width of each class as

three hence the first class is taken as 0 to 2 and then 3 to 5 6 to 8 9 to 11 12 to 14 15 to

17 as the maximum observation is 15 we stop here now place the tally marks the first observation is five hence the

tally mark is placed in the class 3 to 5 the second observation is three so we put tally mark in the CL class 3 to 5

the third observation is three so put tally mark in the class 3 to 5 the fourth observation is 1 so put tally in

0 to 2 proceeding similarly we group all the values after grouping all the values we

count the tally bars and write the frequencies in the frequency distribution the minimum value of the

first class is zero and the maximum value is 2 here 0 is called as the lower class limit and two is called as upper

class limit similarly for the second class three is the lower class limit and five is the upper class limit so

on in this grouping both the lower limit and upper limit are included in the same class such a grouping is called as

inclusive class interval let us consider another example the data of daily wages of the workers

in a factory manufacturing Plastic Products form a frequency distribution taking lowest class interval as 90 to

140 with a magnitude of 50 for the given data we shall construct the class interval starting with 90 and

width of 50 units here the upper class limit will be 140 the next class interval is 140 to

190 then 190 to 240 240 to 290 290 to 340 340 to 390 390 to 440 40 as the maximum value is 425 we stop here now

the value 100 is between 90 to 140 so we place a tally mark in the first class the value 115 is also between 90 to 140

hence we place the tally in the first class next 120 125 92 also lies between 90 to 140 hence they are also grouped

under first class now observe the value 140 140 is the upper limit of the first class and lower limit of the second

class if 140 is included in the first class the width becomes 51 hence 140 is included in the second class so all the

values of the data are grouped and the frequency table is obtained in this grouping the lower

limit is included in the class whereas the upper limit is excluded such a grouping is called as exclusive class

interval for any of the classes if the lower limit of the first class or the upper limit of the last class is not

specified then such a class is called as open-end class CL es in the above examples the class width were

specified in case if the width is not specified then the class width and the number of classes are decided based on

the rule given by STS we shall discuss this with the help of an

example consider the data related to the number of automobile parts produced by the workers in a factory on a certain

day now we have to construct the frequency distribution table where the class width

is not specified in order to decide on the number of classes we apply the Formula 1

+ 3322 log n to base 10 where Y is the number of observations in this example

we observe that Y is 100 on simplification we get number of classes as 7.

644 which is approximately equal to 8 now we shall decide on the width of each class width is given by maximum

value minus minimum value divided by number of classes for the given data we have maximum value is 46 minimum value

is 13 and the number of classes is 7 644 on simplification we get width as 4.55 let us approximate it to five for

easy grouping now construct the class intervals as 10 to 15 15 to 20 so on

till the maximum value is covered now grouping the values using the tally mark As explained earlier the

frequency table is obtained the midpoint of each class is obtained as lower limit plus upper limit

divided by 2 so here the midpoint of the first class is 10+

15 is 25 25 ided 2 is 12.5 the midpoint of the second class is 15 + 20 that is is 35 divided by 2 which

gives 17.5 so on the midpoints of the other classes can be

obtained from this example note that the number of observation in the class 10 to 15 is 2 that means all the two

observations are less than 15 in the class 15 to 20 the number of observation is 7 and the number of

observations less than 20 are 2 + 7 that is 9 in the class 20 to 25 the number of observations is 14 and the number of

observations less than 25 is 2 + 7 + 14 that is 23 the successive total of several frequencies is termed as

cumulative frequency and if it and if it specifies the number of observations less than a

particular value it is termed as less than cumulative frequency now observe that the number of

observations in the class 45 to 50 is three and all the three observations are more than

45 the number of observations in the class 40 to 45 is 12 and the number of observations more than 40 is 12 + 3 that

is 15 similarly the number of observations more than 35 is 16 + 12 + 3 that is 31 so if the cumulative

frequencies specifies the number of observations more than a particular value it is termed as more than

cumulative frequency the frequency density is given by frequency of the class divided by width

of the class and the values are as shown in column 7 the relative frequency is given by

frequency divided by total frequency and is as given in column 8 and the relative frequency multiplied by 100 gives the

percentage frequency by variate frequency distribution in many situations we are

simultaneously studying two variables from the same population the data so obtained as a

result of this cross classification gives rise to byari frequency table let us understand the construction of the

bivariate frequency with an example the data is related to the ages in years of newly married husband and

and wives are considered here we have two variable one is age of husband and other is age of

wife let us denote the age of husband as ex and age of wife as why in the given data the minimum age of husband is 24

and the maximum age is 28 the minimum age of wife is 17 and the maximum age AG is 20 we shall consider

the age of husband in captions and the age of wife in stops now observe that in the first pair

of observation the age of husband is 24 and the age of wife is 17 hence place a tally mark where 24 and 17

meet the second pair of observation has the age of husband as 26 and age of wife as 18 so place a tally mark in the cell

where 26 and 18 meet proceed in the same way till all the 20 observations are marked now count the tally mark in each

cell and indicate them in braces which indicates the frequencies now the frequencies

corresponding to the X variable is called as marginal frequency of X and the frequency is corresponding to the Y

variable is called as marginal frequency of Y this is tabulated as

shown now we shall look into the conditional frequencies writing the frequencies

values of a variable for the fixed value of the other variable is called as conditional

frequencies in the above table suppose if we want to know the number of bir in the age of husband whose wife age is

18 years then we fix the age of wife as 18 and write the frequencies corresponding to the age of husband

similarly if we want to know the number of persons in the age of wife whose husband age is 27 years then we fix the

age of husband as 27 and write the frequencies correspond ing to the age of wife the frequency obtained is as

shown summarization in this session we have discussed about the classification the rules of classification and the

different types of classification the process of tabulating the data and the techniques of proper

tabulation has been discussed along with different types of tabulation the data can be grouped based

on the number of times an observation is repeated and is done with frequency distribution under frequency

distribution we have discussed the concepts of univariate and bivariate frequency distribution and the terms

associated with it thank you [Music] [Music]

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