Standard Deviation - Statistics

today we are going to start with the concept of standard deviation now it is a very important topic in mostly class 11 and class 12 syllabuses also applicable for cpt exams and a lot of become exams also so depends on what whatever you are pursuing but standard deviation is a very important topic and consists of approximately five to ten marks depending on your course for your respective exam now regarding standard deviation let me tell you beforehand you need to know arithmetic mean in the best possible manner if you don't know arithmetic mean check out the other video for arithmetic mean completed and if you already know it well and good we'll start with the concept of standard deviation now before explaining standard deviation let me tell you there are some topics in statistics which are better understood with understanding the definition itself like if you know what mean is it will be helpful in the computation also if you know what mode is it will be helpful in computation also but there is not much help if you mug up the definition of standard deviation if you try to understand standard deviation it will take you a lot of more much more time you know it will consume more time then what time it will take you to just learn up the formula and do the sum so I will recommend you directly start off doing the sums with the formula and during the course of time you get to understand the formulas better or the sums better but first all you need to get concerned about is the marks that you have to score and then regarding the concept you can do it anytime you want okay so first in tough topics like standard deviation index numbers or whatever be it I'd recommend first go with the formula mug it up start off with the sums and then you'll gradually get the concept cleared okay so we'll start off with the concept of SD or standard deviation now standard deviation short for miss D is denoted by the alphabet Sigma now many people have this confusion whether this is Sigma or this is Sigma this is summation and this is Sigma so Sigma is standard deviation summation is the sum total of a given series now there are a lot of formulas concerning standard deviation a whole lot of formulas approximately sometimes in a book 6 to 7 formulas are present actual mean method direct mean method continuous series method grouped method ungrouped method but there is a very short and easy way to get along with standard deviation with just two formulas only two formulas are required in total to cover up standard deviation yes there are complexities there are complex formulas sometimes in your board they recommend you to do it in a tougher manner but the easiest two methods direct methods to directly get the marks in any Higher Secondary exam there are only just two formulas that you need to learn no other formulas okay now these formulas will work on a very nice suggestion basis as in there will be only some sums that are expected to come as in continuous series sums are most mostly expected to come in frequency distribution or in standard deviation sums those are basically five Maxim's or six Marx sums as per your syllabus so we already sketch out whatever is going to come and we leave out whatever is not going to come so you need to exclude those from your syllabus yourself even though the school or the college will tell you to you know make up all the formulas just directly learn these two formulas and you'll automatically see it's like 90% helpful in your entire okay so the first formula that is applicable for individual series is standard deviation is equal to root over summation D square by n this is the first formula and the second formula for continuous series or grouped method whatever they call it make this capital n root over summation FD square by capital n - within brackets summation FD by n whole square this has a particular difference this whole square means another thing and this square means another thing this means either make way NQ / could square Nahan no squares are required / total number of frequency now beforehand before in the previous topics and previous classes I have told you the difference between small N and capital n just a brief recap small n is equal to number of observations and capital n is equal to total of frequency so let's take up a some first for individual series we'll write down the formula here it's always better to write the formula at least once in your sum whenever you are doing the statistical based some or even a mathematical sum you know the teachers prefer that you at least write down the formula ones sometimes they give you step marking for this keep that in mind so let's take any series say the given number of series is say find the standard deviation of say 5 10 25 30 50 this is the question that we have the best way to solve a statistical problem is in tabular format hence will make since only this these series are given these numbers are given will create a series out of it 5 10 25 30 50 we already know n here is equal to number of observations and here the number of observations is equal to 5 1 2 3 4 5 5 total numbers have been given 5 observations now what do we need is D D is equal to deviation or X minus X bar X minus X bar means here X bar is equal to the mean of the series if you still don't know what mean is please go check out the mean video and now I am assuming if you know mean first we'll find out mean in the same method we used to do mean in individual series so the formula for finding out mean or x-bar is in individual series summation X by small n total of this series find out 5 plus 10 plus 25 plus 30 plus 50 it's coming down to 120 120 by 524 this is the arithmetic mean that we need so now we can prepare another column D which is equal to X minus X bar is always prefer to write it down here what the formula is for and now 5 minus 24 individually try to yourself since we require summation D square that means we need to find out the squares of each and every deviation so 19 minus 19 square minus 14 square now whenever we are trying to square a negative digit it automatically converts into a positive one because negative negative is positive so 361 196 136 and 676 the total of all these numbers will give us summation d square calculate the total one two seven zero check if it is right or wrong one two seven zero it's coming down to one two seven zero done now we will use the formula this formula so s D is equal to root over 1 to 7 0 by small and what is small in here 5 total number of observations 5 start dividing first divide then try the square root use calculators if allowed if not use the long method for calculation approximately fifteen point nine three seven fifteen point nine three seven so what we are doing here is basically standard deviation first you have to write down the formula then you only have to find out whatever is required sometimes I've seen people trying to find out extra columns or not being able to judge sometimes you might also face the same problem about judging what values we require whether to total this column or not the best answer to this is check the formula separate out individual units that you need here only what we need is summation D Square and the small n nothing else so small n is five for summation d square first you need to find out D but did they ask for the summation D or anything so you don't need to total this it's useless so first find out D then D square well ad Nikola Jeffrey D square squares for total one two seven zero if we divide Cartesian number of observations whose Cavazos cos square root calculator allowed to well and good that that will be very easy when he allowed her to through say o'clock practice car without calculator NATO exam my bought butter problem create was either okay nahi hatha auger calculate Karnataka please kiss ECC collegio I friend say they will guide you with it we put a method clear this is very easy so next will be taking up continuous series continuously iske formula public law now in this particular observation in this particular equation there is something important here we have written summation FD square by n I need to focus on this thing for a moment because here what we mean is summation of frequency multiplied by deviation square many people multiply F and D and this square square it up and then find out the total that is wrong that is not what we want what we want is frequency multiplied with deviation square so we need to find out D first then square up the D multiply it with F and then find out the total we don't need to square it up together first D then D square Pella DS pellicle de colina for d square Nicolini was co frequencies are multiplied Karina through Scott total Nicolini take a yapper FD square comma Club F into d square chikka some carrying your clear ajay gamma giriboy other Aetna yeh total is particular observation square mania chicken start Karthik easy so example later best preferred a up lock the shots at mcaro solve it according to what I am writing on board it will be much more better for you class frequency these two are usually given 0 to 10 10 to 20 I'll take any just random numbers fine this sum is no reference from any book so just made up so next what we need to find here is f is given what we need to find here is X X usually denotes mid value so 10 plus 0 10 divided by 2 5 10 plus 20 30 divided by 2 15 20 plus 30 50 divided by 225 similarly these fine keep following whatever I am trying to say next we need B what was the formula for D same in Lhasa ax minus X bar what is X bar the arithmetic mean what is the formula for continuous series for arithmetic mean direct method summation F X by capital n what do you mean by capital and total frequency what is the total frequency here 10 summation F X so we need to find out F X also for now I am just erase the formula let's find FX first that means F multiplied with X 1 into 5 15 into 225 into 335 into 3 go on keep doing this total of FX compute 260 so 260 divided by 10 gives us 26 this is the arithmetic mean so now here 5 minus 26 26 is the arithmetic mean that we got here B is equal to X minus arithmetic mean excess weight 5 here 5 minus 26 is minus 21 then again 15 minus 26 25 - 26 individually we'll have to write down the more you write the more chances of not cutting off your marks 2:19 sorry so the question is I'll put the formula here now do we require the summation of D answer is no do we require the submission of X answer is no so you'll have to judge whether to compute the total or not till now these were required we took up the answers of these but this is not required this is not required so we will not get into the computation of the same because in exams we'll have a very short time in hand for these silly computations we cannot waste time no extra marks are provided for it no extra marks are cut for it fine so we have D right now what we require now is FD d square and FD square we have capital n so first anything you can do I'll start off with say FD do not confuse between the columns so minus 21 into 1 same - 11 into 2 minus 22 minus 1 minus 3 27:19 we need to compute the total for this next find out D square that means minus 21 into minus 21 minus 11 into minus 11 start doing it then total of this total of d square is not required total of d square is not required we need the total of FD square so make another column FD square so many columns are coming in you need to manage it properly a chessick Alva kya kiya Kwanzaa column focus casat multiply choreo egg bar X photos of mr. Coley aapke purified mangia what what does the examiner want an answer a simple answer approximation alpha of smoggy answer maybe okapi Chioggia licking sada off scale silica couch gala toga step marking it for an examiner already to see so many figures is irritating you cannot expect our fight for step marking in these things if you are doing statistics either do the complete chapter properly or just have the theory portion in control don't leave it half way so FD square start multiplying frequency with d square so 1 into 441 now this is a big board so I am being able to manage it even if I cut down on my handwriting I will be able to manage in your copy if you cannot handle it in the portrait mode switch to landscape it's allowed in any examination it's allowed don't worry about it switch to landscape if you see a 5 max statistics um you have to remember that it's going to be lengthy switch to landscape mode it's not going to do any harm ok so practice also in landscape it's either ways it's going to take double spaced now what happens is if you have a sheet like this and if you do half the columns here and then start of the second half columns here these two columns are never going to match you are bound 85 percent times to make a mistake don't do it switch to landscape so FD square first is 441 121 into to 242 3 3 into 81 243 then last one is 361 give me the total first one two nine zero now if this is coming to zero it's alright if this is having a positive figure it's good if it is having a negative figure do not freak out it is still correct it might happen so many after so many calculations it might happen the total of something is coming zero or something is coming in negative does not matter once you put it in the formula you will get the correct answer be patient don't freak out if it's negative and please maintain the negatives that we have fine always remember the negatives do not go away anywhere till it is squared fine so you'll have to live with the negatives don't ignore it otherwise the answer will be completely different let's put it in the formula so summation FD square summation of d square is this one two nine zero so first d nicolay d square FD square total of f d square summation f d square one two nine zero divided by what is capital and total frequency that is ten minus now this square is outside of the brackets so what we need here is summation FD the total of FD 0 divided by n again 10 now this whole thing will come down to zero this thing only this portion so what we write do not skip a step divided by 10 minus zero is equal to compute root over 129 use calculators will come down to approximately eleven point three five maybe three four something something you can always round it off at least two digits keep original otherwise you can round off any other digits you want fine now these two formulas that we have discussed are applicable to almost every other sum you take up any sum start doing it but yes some critical sums like ungrouped method unequal class intervals those have some specific formulas now in different boards different syllabuses different formulas has been used so I cannot generalize the formula that you have to use because it will be much of a hectic I don't want to teach you like seven seven to eight formulas like you'll understand them individually but you'll mess up very bad so it's it's just of no use these two formulas are 95% x used these are the like confirmed formulas that are about to come I am totally certain about it so these two formulas this this is the expanded formula used for continuous series grouping method and the first formulas for individual series use them score well best of luck for your exam and like and subscribe for these videos to stay updated with new videos and soon economics for class twelve videos will also be coming up some accounts video will also be coming up and if you need help in index numbers or any harmonic mean or geometric mean series then another sir has discussed am racer he has discussed each and every video each and every statistical and mathematical topic

Channel: Sagar Jain

Views: 573,330

Rating: 4.7232041 out of 5

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Id: eeRrNT7DUHk

Length: 27min 34sec (1654 seconds)

Published: Sat Dec 02 2017