 I have two people till now you have given me attendance just seven views now give your attendance quickly okay four people till now I will wait for two more minutes guys and then I will start okay Varsha okay we will start people are not joining therefore so I am starting with topic statistics now what is statistics statistics is a form of science which deals with I am writing the definition form of science which deals with selection, presentation analysis and representation of the data or let's say interpretation because presentation I have already also important words in this particular definition is first of all collection, presentation, analysis and interpretation and then comes the word data now why statistics now try to understand I want to know a pattern of which math book grade 9 students across India CVSE board wanted now if I want this information to be with me what I will do is I will start collecting data and what would be that data so data would be I will go to student to other and I will start asking which math book do you prefer somebody will say Aadi Sharma somebody will say R. S. Agrawal somebody will say Piyasan publication somebody will say N. C. E. R. T. somebody will say autonomous board work so what happens is I will have some good 10-15 categories and suppose I am interviewing some good 10 lakhs people so what happens is I have 10 lakh data in front of me now I need to so collection of data this is the part of collection of data presentation of data is last actually so first I am doing analysis so my analysis would be that I will categorize data into different categories so I will say out of 10 lakhs 2 lakhs read Aadi Sharma 2 lakhs read R. S. Agrawal 1.8 lakhs read Piyasan and likewise I will do the filtering of data and then I will make a chart so interpretation of the data is that the most number of people are studying either Aadi Sharma or R. S. Agrawal 40% people are studying Aadi Sharma and R. S. Agrawal very less people are studying autonomous board book and all those things so having said that I will have then presentation of data and the presentation of data will say me that see here I made a bar graph which is of 2 lakhs for R. S. Agrawal similarly I make a bar graph which is again 2 lakhs which is for Aadi Sharma this is 1.8 lakhs for Piyasan and likewise so statistics is gathering data from somewhere and with that data I study that data properly put it in a certain format depending on my requirement and then try to find out behavior try to find out the habit of or try to find out try to find out characteristics which is of my liking so statistics helps us in mining statistics helps us in knowing several unknown characteristics about different surveys now another word in my discussion was data now what is data data is nothing but information or set of given facts this is what data means now as we know data now let me go to type of data so data is categorized into two parts one is primary data and one is secondary data and primary data is something data collected first hand by the investigator himself so in this kind of data one thing is important that when I am going to find out when I am doing the research work when I am doing study about something and I need some information from outside I go out try to find out that data that is what my primary data is all about now this is my secondary data and my secondary data tells me that when I have to study I look to some historical data so this data was collected by someone and not collected at time of research it is collected by someone else so if I give a live example of this every 10 years we have census census means we calculate total population and other fundamental categories like we calculate education we calculate income and all those things is it okay so earning members of the family income is not salary we calculate members of the family whether a person is working he is employed he is not employed then we then other things so what happens every 10 years I have my census of India so this is a primary data secondary data can be that if I go to find out the you can say anything like suppose I go and I have to give a presentation about the unemployment rate in India and I go to NSSO website and I find out data from there and I just copy paste that data saying that I have taken it from NSSO so that data which I didn't collect become secondary data because this was collected by NSSO survey and I didn't use it so sorry I didn't I have nothing to do with collection and analysis of data I just find it from somewhere I quote the source that this is the source from where I am getting it and then I do my business with that so I have already explained primary and secondary data to you now let me move to raw or ungrouped data so raw or ungrouped data means data when you collect the data in original form without any analysis categorization you have to write this word that ungrouped or raw data is always in original form grouped data is it has been put in certain order when it has been put in certain order so that order can be extending order it can be categorized by name address date of birth anything so categorization of data depending on different variables is known as grouped data now there is something called array now array is specific form of grouped data that specific form is nothing about any numerical data if any data set is arranged in extending or descending order that is called array so array means you take the data put it in arranging order or you put it in descending order so you find an array now next thing is frequency of data observation and this is very important guys focus here frequency of data observation it is the number of times and observation occurs so what I do is I will take a few numbers and I am writing few numbers here 5 2 3 1 2 4 5 1 2 3 1 2 3 now first of all if I have this kind of data I know that numbers are from 1 to 5 and I have all the numbers so if somebody is asking me that what is the frequency of each observation I will make like this so remember this and what is this data all about number of children in each house so I went to 20 houses and I found out how children are there in that house so what I will do over here is I will make a frequency table how to make frequency table I am making frequency table is like this you will write number of children then you will write tally mark and then you will write frequency so as this number is going from 1 to 5 all numbers are 1 2 3 4 5 number of children are 1 tally mark is how much 1 2 3 4 5 so tally mark means see what happens I draw 4 lines like this and 1 line like this for 5 so suppose if tally mark let me explain here tally mark if any number or any number is coming once I will make 1 line if 2 numbers are coming I will make 2 lines if 3 numbers are coming I will make 3 lines if 4 numbers are coming I will make 4 lines if 5 numbers are coming I will make 4 horizontal line and 1 diagonal line so this is for 5 what about 6 I will make 1 line for 7 I will make 2 line for 8 I will make 3 line for 9 I will make 4 line and for 10 again I will make 1 line like this so this is how you have to make tally mark so this gives me frequency is equal to how much 5 so now I will remove number 1 from here I will go to number 2 so this is coming 1 2 3 4 5 6 so for 6 I will draw 4 vertical line 1 line like this and then again 1 line so this is 6 now I will go to 3 so 3 is coming 1 2 3 4 times so 3 is coming only 4 times so I will draw 4 vertical lines so I got 4 vertical lines now I will go to 4 4 is coming 1 2 3 times so for 4 I will draw 3 lines and I will write 3 here and for 5 I will write 1 on this side and 1 on this side so I have only 2 so I will make 2 vertical lines and I will write 2 here this is what my frequency table is did you guys understand just let me know in the chat box I am waiting ok Shraddha Ritu has told yes Dhruti has told yes Varsha has told yes Anchita did you understand Tanay Tanay is also saying yes good ok so let me move to few questions and then I will come to exclusive inclusive form ok so fine all of you yes so I am moving questions I am moving 2 questions so look at the second example I am doing it for you and I am directly taking example from your book R. S. Agarwal this says that the following data gives marks out of 50 obtained by 30 students of a class in a test and this is like this so let me write with a green pencil the data is like this 40 12 46 37 17 36 22 23 19 39 25 5 33 19 21 12 41 17 19 17 again 12 8 10 21 13 14 16 17 18 19 20 26 28 28 29 30 30 31 32 33 34 35 36 37 38 39 39 40 40 41 42 43 45 47 49 50 50 51 51 52 53 raw data is Condensed, so this is called class interval now see how I'll take class interval here So my number varies from 1 to 40. So I can take class interval of 1 to 5 then 6 to 10 then 11 to 20 Then sorry 11 to 15 because this this class size has to be equal most of the time Class size is difference between the bigger number and the smaller number. So I'm taking a class size of Five and here 16 to 20 and likewise I can take till 40 or I can take a class interval of 1 to 10 then 11 to 20 Then 21 to 30 and then 30 1 to 40 now guys look at here Look at very carefully here I am ending this class interval at 10 and I am beginning this class interval with 11 What about numbers between 10 and 11? So numbers between 10 and 11 cannot be fit in this particular class interval. So this kind of Arrangement of class interval is good for those data set Where I only get integer values. Are you understanding? So if I'm getting integers, there would be no number between 10 11 20 and 21 30 and 31 So this will do my job If I have any number such as 10.5 So I will not be able to fit it in this data So for that, I'll have to make another kind of data set which is one 10 where 10 included I can write like this that 10 is included here or 10 is not included here And then I'll make from 10 to 20. So I can write that this larger value is not included here So if any number 10 is coming, I'll write here Then I can take from 20 to 30 and then I can take from 30 to 40 Now in this kind of data class interval, what happens? There's some kind of data where I have decimal values So if 10.1 is coming, I know that this is between 10 and 20 So I'll put it here and if 9.9 is coming. I know that this is suited for this data So I'll put it here Which is not possible in this case if 10.1 is coming Where will you put this finishes at 10? This is starts at 11 So I will not be able to put decimal data So now try to understand that this kind of arrangement where I don't leave any gap between the class interval Is known as continuous form or exclusive form So this kind of let me just this is known as continuous form or Exclusive form and this kind of arrangement where there is a gap between The two class intervals is known as non-continuous or inclusive form Now one thing is important to know that wherever you are only getting Integers you can utilize any of these wherever you are only getting You are getting few decimal values also you have to utilize continuous one Wherever you you have data where only integers are there you can take this only this Both of them are fine for integer data but for non-integer data only this one is fine So now let me move to arrange arrangement of the given data into frequency table So I am taking look at here I take class interval There is no need to make tally marks here class interval And I will make it in both both the forms So first one is form So in exclusive form what happens I take from 0 to 10 10 to 20 20 to 30 And this is number of students which is frequency So try to understand let me put data here So now 0 to 10 how many values are there I am saying that 10, 20, 30 are not in here So 10 is not included here 20 is not included 30 is not included It means that if 10 is coming I will write in the second if 20 is coming I will write in the third 30 is coming I will write in the fourth So between 0 to 10 let me find out value So till now I have not got 1 this is 1, 2 I have got till now 2 After that this is the third one Then after that this is the fourth one I told 10 I will write in the second one so this is the fourth one Fifth one and sixth one so I have 6, 6 numbers So 0 to 10 I have 6 numbers Now let me go to 10 to 20 and any 10 would be included 1 I have 2 then I have 3 then I have 4 Then I have 5, 6, 7, 8, 9, 10, 11 So I have 11, 10 to 20 Similarly if you count 20 to 30 you will have 20 to 30 if you see you will have 1, 2, 3, 4 and 1 more 5 So this gives me 5 Now there are few numbers more than 40 also So I will have 40 to 50 also because the number is still 50 So this is 5, 30 to 40 I will have 1 here and 2 here, 3 here and 4 here So 4 numbers between 30 to 40 40 to 50 I have 1, 2, 3 and 4 So I have 4 numbers here So 40 to 50 I have 4 numbers Now what you should do is that after making this frequency table This number addition of these numbers Frequencies should add up to 30 So 6 plus 11 plus 5 plus 4 plus 4 Is 17 plus 5, 22 plus 8, 30 So I get a number 30 here Now let me make the same table in non-exclusive format Yes, non-exclusive format or inclusive format So inclusive format means now I will not have that Problem of where I should fit 10 So I write class interval here And this is from 0 to 10, 11 to 20, 21 to 30 And 31 to 40 and this is frequency The frequency is telling me that 0 to 10 So 0 to 10 what happens is here Initially I was putting 10 over here Now I will have to put 10 over here So over 6 in the previous one Here the frequency was 6 because I put the 10 over here So I will add 10 over here, frequency becomes 7 And here it was 11 in the previous case I will remove 10 from here So this becomes 10 Now what happens is here 30 was not included 1 max 30 which is here Now this will have to be included here So if I include it here This gives me 6, this gives me 4 And 40 to 50 gives me 3 So this gives me how much? 30 So this is it Solve the first question of this type from your book First question of frequency distribution from the book Have you done? Okay guys have you done? Okay fine So let me move to another topic Not another topic Let me move to another concept in this thing Now there is one concept which I didn't tell you here Is class mark is from 0 to 10 So 0 plus 10 divided by 2 is equal to 5 So here class mark would be 5 What is the class mark? Class mark is mid value of upper and lower limit Mid value of upper and lower limit And how do you find out mid value of 2 points? If first point is A and second point is B Mid value would be A plus B divided by 2 So this thing comes like that 0 to 10, 11 to 20 you can find out the mid value That's simple Now let me go to some other question So let me give you a question now So question 4 is The water tax bill in rupees of 30 houses Locality are given below So this is 144, 184, 130, 195, 132, 134, 196 114, 212, 174, 188, 210, 202, 145, 175, 154, 174, 178 166, 146, 135, 115, 120, 114, 140, 188, 176, 166, 210 and 208 So you have to construct a frequency diagram or frequency distribution table with class size 10 Just do it After you are done, just let me know in the comment box Okay, Sradha has done it Okay, I've got only one answer till now I'll wait for 2 more minutes Okay, so I've got few answers now Sradha, Ritu, Ruti and Tanay Okay, let me solve because I have to finish off other topics as well So how I approach this question It is very important when a question is discussed to know about approach Now approach of this question would be First, how many days are there? So 30 houses So total number is 30 Now, frequency size of 10 It means what? So you look at here I'll start from the lowest number What is my lowest number? If I go through this I find that 114 is my lowest number which is coming 2 times What is my highest number? So highest number in this line is 212 So any other number more than this I don't find it So it means that I'll start from 114 I'll write till 124 Then 124 to 134 Then 134 to 144 Then 144 to 154 Then 154 to 164 Then similarly 64 to 174 Then similarly 74 to 84 84 to 94 Then 94 to 204 And then 204 to 214 This is how my frequency class intervals look like Now once you have made these class intervals Now what we need to do is In your book it has been given I don't do it generally But as your book suggest You make tally marks So tally marks And then you write your frequency So once you write your frequency You will see that 100 And I'm not getting into calculating each and every number You will see that 114 to 124 If you count here There would be 4 numbers 124 to 134 There would be only 2 numbers 64 to 144 There would be 3 numbers 144 to 154 Again there would be 3 numbers 54 to 64 There is only 1 number So I'm drawing 1 here 64 to 74 There are only 2 numbers So I'm drawing 2 numbers 74 to 84 There are 5 numbers So 1, 2, 3, 4, 5 So there are 5 numbers 84 to 94 There has to be 3 numbers 94 to 204 There has to be 3 numbers And 204 to 214 There has to be 4 numbers So how much it is? This is 30 numbers That's simple So this is how you have to do it Now in this question only I'll tell you concept of cumulative frequency So what is cumulative frequency? One I have made this Frequency diagram The cumulative frequency is I have to keep on adding the adjacent number So first number there is no number So in cumulative frequency I write 4 But next number this 4 will be added to this 2 Then 6 Now this 6 will be added to next number 3, 9 Again 9 will be added to this 3 This becomes 12 12 will be added to 1 This becomes 13 15 added to 5 20 added to 3 This becomes 23 23 added to 3 This becomes 26 26 plus 4 is 30 So this is how it is So now let me go to another concept Which is Formation of Different type of graphs So I am starting with bar graph Bar graph is one of the most Or one of the simplest This thing Bar graph is nothing but It's of Uniform width Wearing height So What do I mean by height Height represents The frequency of Corresponding observations Now look at here This is mode of transport So mode of transport is car Bus Moped Then Bicycle And then I have rickshaw And then I have here number of Students travelling Through these modes So car I have 4 people Bus 27, moped 11 Bicycle 20 and rickshaw 8 Now what I do over here Is The bar graph Now look how I draw the bar graph The bar graph would be drawn like this On x axis I will put here Car Then I will put here bus Then I will put here moped Then I will put here bicycle And then I will put here rickshaw When you make this x axis Make sure that This Intervals Intervals are equidistance from each other It should not be that car you are Making here and rickshaw And bus you are making here And moped again you are making here This should be equidistant from each other Also when you are selecting Scale on y axis It has to be uniform scale So say I say that One unit on the bar chart One unit on the graph is equal To one Number here Let's say one unit is equal to two numbers here So what happens One unit is two numbers So this becomes 4 Then this becomes 6 Then this becomes 8 Then this becomes 10 12 14, 16, 18 20 22, 24 26 This is nearly 27 So car is still where If you make like this Make sure this width is of equal length So 0.5 0.5 centimeter, 1 centimeter nearly Then you will have bus Largest so this will be 27 Like this Then you will have moped 11 11 come somewhere here So moped would be somewhere like this Then you have bicycle 20 So 20 is somewhere here So bicycle would be somewhere like this 20 rickshaw would be 8 Like this So this is how you make your bar graph So once I have done the bar graph Okay from bar graph topic Solve one question Open out your RS Agarwal book Take a question from bar graph Topic and try to solve it Gruti I am saying from bar graph Bar graph topic Solve one question That's what I am saying The chapter number in my book is different From chapter number in your book The chapter number Solve one question from your bar graph book RS Agarwal So Radha has done it Most of you are saying done sir So I am moving to another topic Which is Histograms Now bar graphs if you could have seen Bar graphs the variable was Discrete What do I mean by discrete variable Discrete variable means Something which is Where numeric Values does not matter I mean there you saw Car moped all these things were Given what happens When you get Exclusive Or Sorry exclusive Or continuous Distribution So For that if I have to make A vertical graph like this I have Frequency Distribution I am writing here Distribution So I am writing marks And I am making class interval here So this is 10 to 20 This is 20 to 30 This is 30 to 40 40 to 50 50 to 60 70 70 to 80 And this is number of students So number of students is 7, 11, 9 13 16, 4, 2 So First of all let me tell you what is a histogram Histogram is a graphical Representation of frequency distribution In the form of rectangles With class intervals as Bases and the corresponding frequency As heights Now This looks like a simple definition But what I mean to say is that When there is this Exclusive class interval Then only histogram comes into picture So what I do over here Is you look at here I make Histogram like this Now you look at here The histogram will start from 10 Because between 0 to 10 There is no data So between 0 to 10 I make this kink Don't forget to make this kink kink says me that the data Or the graphical representation Doesn't start from 0 So I make this kink here After kink This is 10 and this is 20 So 10 to 20 There are 7 data So I make this data 10 to 20 Now the other number And the number of data is 11 Suppose it is here Now what I see here is This data is finishing on 20 And this data is starting on 20 So this 20 data only will be Increased to 11 And then this will be 30 Now 30 to 40 I write here So again this 30 is common between here to here So the other number Which is 9 will start from here And it will go like this 50 is 13 so 40 to 50 Will be somewhere like this 13 so this is 50 Now 50 to 16 16 So this is somewhere like this 16 So What I will do now is Now 64 So somewhere like this And 70 to 80 is 2 So this is somewhere like this So this is how you make histograms Now take one question from your book Of histogram try solving it From histogram select first question And try solving it Every time I am mentioning book I am mentioning your R. D. Sharma Sorry R. Sagarwal Every time I am mentioning A book I am mentioning R. Sagarwal So solve the question Okay 5 people have told me they are done I am waiting for others One more minute Okay so now I am not waiting anymore Let me go to another topic Which is frequency distribution Sorry frequency polygon I am sorry Another way to represent Data graphically Is to make frequency polygon And how to make frequency polygon So look at here Now one thing you should remember That frequency polygon Starts from 0 On x axis And ends at 0 On x axis So try to understand what to do then So look at here So let me write This is Let me make this is my Pocket expense And this is Number of students 0 to 5 10 5 to 10 16 10 to 15 Is 30 15 to 20 is 42 Now 20 to 25 Is 50 5 to 30 is 30 30 to 35 is 16 And 35 to 40 is 12 Now when I need to go to make Frequency polygon What I do is Look at here what I do is In frequency polygon So I See what happens frequency Is this kind of graph Where you have to plot Points with respect to certain Number it's not this In frequency polygon This complete range or class Interval will not be used Frequency polygon is a line Graph like this something like this The number is going from here to here So I make numbers like this And then I do like this And something like this Then I come from here Then I stop here something like this So frequency polygon is something like this Where any particular Number like this number 10 Number Plotted against one singular Point on x axis It would not be plotted against A class interval like in histogram What happened that Any number was plotted Against class interval This will not be case Here in frequency polygon So what did I do in this particular case One thing That I will be doing is That As I have to find out A specific point On x axis There is something Called Class mark which will be calculated So class mark As I already told you Class mark would be So rather than making this table I will make the class mark here only So Class mark would be You look at here 0 plus 5 by 2 is 2.5 5 plus 10 by 2 is 7.5 So I am calculating here Class mark And 10 plus 15 so this gives me 7.5 This will give me 17.5 This will give me 22.5 This will give me 27.5 This will give me 32.5 This will give me 37.5 As simple as that So This is it Now I make this Pocket expense So pocket expense is From range 0 to 5 I am leaving this row For now Class mark is 16 And I keep on making this Now what happens is If I have this kind of data In front of me So let me just erase it for some time And let me make frequency Polygon for you For frequency polygon what I do Is Draw this x axis Now on x axis For these points 7.5 12.5 17.5 22.5 27.5 32.5 32.5 And then I have 37.5 So on 2.5 On 2.5 I have 10 here On 7.5 I have 16 here On 12.5 I have 30 here On 17.5 I have 42 here On 22.5 I have 50 here On 32.5 Which is 16 here So it will be somewhere here 16 And on 37.5 I have 12 here So 12 would be somewhere here So what I will do is I will start my graph like this And I will start joining different points Once I join different points I get this kind of frequency polygon here Now the problem is I told that the frequency polygon always Starts from 0 and ends from 0 So what do I do in that case So what I have to do in that case Is that When I am making the class mark Class mark is starting from 2.5 Look at the Look at the class interval The class interval is of 5 So what I do here is that From 2.5 I will write So I will write class interval 1 before it And 1 after it So what happens is Before it the class interval Would be from minus 5 to 0 And after it the class interval Would be 40 to 45 Now class 5 of minus 5 And 0 is minus 2.5 And class Mark of 40 to 40 40 and 45 is 42.5 So this will start from here Which is minus And this will go Till 42.5 So as My actual Frequency polygon is this I have to start it from 0 So I will go back This class interval is of 5 5 places like this And I will go ahead 5 places Like this and I will match it with x axis This completes my frequency polygon So that is not That it follows from histogram There is nothing like follows Frequency polygon Can be made With histogram Frequency polygon can be made Separately also As I have done on the board Right now There is nothing like it It follows from histogram So take one question Now from your book and try solving it Okay 4 people have written they have done I am waiting for others Okay fine So what I do is now I teach you This will be the last topic Mean median mode I will take In Thursday's class with probability Because probability will not take more than To complete at your level So maybe half an hour more You will see what to do In class because that Would be the last class Now How to make So histogram Frequency polygon In same graph So Suppose I give A table I make a table here I am sorry So you know the heading I am removing the Heading Let me make a line over here And then I have another line here Another line here I have another line here I have Another line here What I do is I give Cost of Living here and then I have 1, 2, 3, 4, 5, 6 So 1, 3, 5 And 6 So what I do now is I have Cost of Living here This gives me Number of workers So I give you a range here This is 140 to 150 And Here 5 people are there And this is Cost of Living has been given in terms of Rupees 150 to 160 I have 10 160 to 170 I have 20 170 to 180 I have 9 180 to 190 I have 6 190 to 200 I have 2 Now what I do is I draw the Histogram first To draw the Histogram what I will do is I will plot my X axis and Y axis Now You see here the X axis Starts from 140 So I will have to make this King says me that This doesn't start from 0 So I will draw 140 to 150 and this is 5 Like this Then I have 150 to 160 Which is 10 like this 120 like this Then this is 9 Then this is Nearly 6 And this is nearly 2 So I plot it here this is 140, 150 160 170, 180 190 and this is 200 What happens over here is This is my Histogram But what about frequency polygon In the same graph So for frequency polygon I know that I need the class mark So here class mark would be 145 Here it will be 155 Here it will be 165 Here it will be 175 Here it will be 185 Then here it will be 195 So I put it here As 145 So one thing is here In between I will just have to put This is 145 So in front of 155 I put another data This is 165 I put it here This is 175 I put it here 185 I put it here and 195 I put it here And then I start matching this Something like this And once I match this data My frequency polygon is half ready And why it is not half ready Because what happens is I have to put it across On the left hand right to 0 And this is 145 The class interval is of 10 So I put it at 135 And I put it on This side on 205 Why I am taking it beyond 10 Because previous interval I told that go to previous interval It is 140 to 150 It will be 130 to 140 on this side And this will be 200 To 210 on the other side So class mark Of 130 to 140 would be 135 And class mark of 200 to 210 Would be 205 So let's go to 135 here And let's go to 205 here So this gives me 135 And this gives me 205 So This is how it is So this is how you make Solve one question of Where you have to solve frequency polygon And histogram together And then we will meet up on Thursday To take the discussion forward That would be the last class I will be finishing the syllabus And then we will move To revision Revision A few people are saying That they have done I will wait for others Why few people Five people have said they have done So let's do one thing guys Stopping here I have to finish Only mean media and more Which will take not more than half an hour I request all of you to carry Your RS Agarwal book In class on Thursday Please carry it for one class Because I will just finish it off that day And If you have any doubt Do let me know now So that I can repeat things So I am waiting for next one minute If you have doubt this let me know I will repeat that portion for you To explain you again Otherwise I will wrap up the session Just one request I am just repeating it once again That in the next class on Thursday Please carry your RS Agarwal book Tell your friends who are not attending this class That they have to carry RS Agarwal book On Thursday And let's meet Any doubt if you have Do ask me I am waiting for your doubt Now if there is no doubt I will wrap up the session Okay fine So nobody is asking me any doubt So thank you so much for joining the session Fine So see you on Thursday Bye bye