Average general rules and tricks 05-07-2016

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Important Points for Average

What is a average?

In basic terms, midpoints normally allude to the whole of given numbers partitioned by the aggregate number of terms recorded.

बुनियादी संदर्भ में, की मध्यबिन्दुओं सामान्य रूप से दर्ज की शर्तों की कुल संख्या से विभाजित दिए गए नंबरों की पूरी करने के लिए संकेत।

Average = (aggregate of all terms)/number of terms

Normal is the estimation of the center number of any arrangement of numbers.

सामान्य संख्या के किसी भी व्यवस्था के केन्द्र संख्या का अनुमान है।

For instance normal of 1,2,3,4, 5 is 3.

Normal can be computed by entirety of all numbers partitioned by the aggregate number of numbers. Normal of 1,2,3,4,5= (1+2+3+4+5)/5 = 15/5 = 3

सामान्य संख्या की कुल संख्या से विभाजित सभी नंबरों की सम्पूर्णता से गणना की जा सकती।

Which is additionally the center number of the arrangement , from here we can likewise say that in an A.P. i.e number juggling movement the center term is the normal of the arrangement .

जो इसके अतिरिक्त, व्यवस्था के केंद्र संख्या है यहाँ से हम वैसे ही कह सकते हैं कि एक ए.पी. अर्थात नंबर करतब दिखाने के आंदोलन में केंद्र अवधि व्यवस्था की सामान्य है।

Principle 1: In the Arithmetic Progression there are two situations when the quantity of terms is odd and second one is when number of terms is even.

सिद्धांत 1: अंकगणितीय प्रगति में जब पदों की मात्रा करीब है और जब पदों की संख्या भी है दूसरे से एक है वहाँ दो स्थितियों रहे हैं।

So when the quantity of terms is odd the normal will be the center term.

What’s more, when the quantity of terms is and still, at the end of the day the normal will be the normal of two center terms.

तो जब पदों की मात्रा अजीब है सामान्य केंद्र कार्यकाल होगा।

क्या अधिक है, जब पदों की मात्रा में है और अभी भी, दिन के अंत में सामान्य दो केंद्र पदों की सामान्य हो जाएगा।

Illustrations 1: what will be the normal of 13, 14, 15, 16, 17?

Arrangement: Average is the center term when the quantity of terms is odd, however before that how about we checks whether it is in A.P or not, subsequent to the normal contrast is same so the arrangement is in A.P.

So the center term is 15 which is our normal of the arrangement.

How about we check it in another way.

In the principal proclamation of the article we have composed that the normal of an arrangement of terms is equivalent to:

Entirety of all terms/Number of terms

So the entirety of all terms for this situation is 75 and the quantity of terms is 5 so the normal is 15.

Presently go to the second shape when the quantity of terms are even

व्यवस्था: औसत केंद्र अवधि है जब पदों की मात्रा अजीब है, लेकिन इससे पहले कि हम कैसे जाँच करता है कि यह नहीं बाद में A.P में है या, इसके विपरीत करने के लिए सामान्य ही है इसलिए व्यवस्था ए.पी. में है के बारे में

इसलिए केंद्र अवधि 15 जो व्यवस्था की हमारी सामान्य है।

कैसे के बारे में हम इसे दूसरे तरीके से जाँच करें।

लेख हम चाहते हैं कि शर्तों की एक व्यवस्था के सामान्य बना दिया है की प्रिंसिपल घोषणा में करने के लिए बराबर है:

सभी नियमों का पूरी तरह / पदों की संख्या

तो इस स्थिति के लिए सभी नियमों का पूरी तरह 75 है और पदों की मात्रा 5 से 15 तो सामान्य है।

वर्तमान में दूसरी आकार करने के लिए जाने के लिए जब पदों की मात्रा भी कर रहे हैं

Illustrations 2: What will be the normal of 13, 14, 15, 16, 17, 18?

Arrangement: We have talked about that when the quantity of terms are and still, at the end of the day the normal will be the normal of two center terms.

Presently the two center terms are 15 and 16, however before that the normal we should watch that the arrangement ought to be A.P. Since the basic contrast is same for each of the term we can say that the arrangement is in A.P.

Furthermore, the normal is (16+15)/2 = 15.5

Principle 2: The normal of the arrangement which is in A.P. could be ascertained by ½(first + last term) Example 1: What will be the normal of 216, 217 , 218?

सिद्धांत 2: व्यवस्था है जो ए.पी. में है के सामान्य आधा से पता लगाया जा सकता है (पहले + पिछले कार्यकाल) उदाहरण 1: क्या 216, 217, 218 के सामान्य होगा?

Arrangement: So the answer would be = ½ (216 + 218) = 217

(Which is likewise the center term of the arrangement)

Illustration 2:

What will be the normal of initial 10 regular numbers?

Arrangement: The initial 10 normal numbers are 1,2,3,4,5,6,7,8,9,10

So the normal will be ½ (1 + 10 ) = ½ (11) = 5.5

Principle 3: If the normal of n numbers is An and in the event that we add x to every term then the new normal will be = (A+ x).

यदि n संख्या के सामान्य एक है और हम हर घटना अवधि के लिए एक्स जोड़ है कि में तब नया सामान्य  होगी (A + x)।

For instance: The normal of 5 numbers is18. On the off chance that 4 is added to each of the number then the normal would be equivalent to __?

Arrangement: Old normal = 18

New normal will be = 4 + old normal = 22

This is on the grounds that every term is expanded by 4 so the normal would likewise be expanded by 4 so the new normal will be 22

Principle 4: If the normal of n numbers is An and on the off chance that we increase p with every term then the new normal will be = (A x p). For Example: The normal of 5 numbers is 18. In the event that 4 is duplicated to each of the number then the normal would be equivalent to __?

सिद्धांत 4: यदि n संख्या के सामान्य एक है और बंद का मौका है कि हम हर शब्द के साथ पी बढ़ाने पर तो नए सामान्य = (ए एक्स पी) हो जाएगा। उदाहरण के लिए: 5 नंबर के सामान्य 18. घटना में है कि 4 नंबर तो सामान्य से प्रत्येक के लिए दोहराया गया है के बराबर होगा?

Arrangement: Old normal = 18

New normal will be = 4 x 18= 72

There are two more operation which can likewise be connected on the same rule as the above, i.e. subtraction and division.

Example 5 : at times, if a number is incorporated into the arrangement of numbers then the normal will change and the estimation of the recently included term will be = Given normal + (number of new terms x increment in normal).

This worth will likewise same as the New normal + (number of past terms x increment in normal ) .

Principle 5: The normal age of 12 understudies is 40. In the event that the age of the educator likewise included then the normal gets to be 44. At that point what will be the age of the instructor?

सिद्धांत 5: 12 की सामान्य आयु 40 घटना में है कि शिक्षक की उम्र वैसे ही सामान्य से शामिल 44. कि क्या बात प्रशिक्षक की उम्र हो जाएगा पर होने के लिए हो जाता है?

Arrangement: Average given = 40

Number of understudies = 12

In this manner the age of the educator = 40 + (12 + 1) x 4 = 40 + 52 = 92

What’s more, this is likewise ascertained as 44 + (12 x 4)= 92

Along these lines the normal age of the educator is 92 yrs

On the other hand

The normal of 12 = 40 that implies the aggregate number of units are 12 x 40 = 480

Presently the new normal is 44 and the quantity of terms are 13 so along these lines the aggregate number of units are = 44 x 13 = 572

So the included units would be equivalent to 572 – 480 = 92

Principle 6 :- at times a number is avoided and one more number is included the arrangement of the number then the normal will change by q and the estimation of the recently included term will be = Replaced Term + (expanded in normal x number of terms ).

सिद्धांत 6: – समय पर एक नंबर से परहेज है और एक और संख्या की व्यवस्था शामिल है तो सामान्य क्यू और हाल ही में शामिल किया जा अवधि = बदला जाएगा टर्म + के आकलन से बदल जाएगा (शर्तों के सामान्य एक्स संख्या में विस्तार )।

For instance: The normal age of 6 understudies is expanded by 2years when one understudy whose age was 13 years supplanted by another kid then discover the age of the new kid

Arrangement: The age of the kid will be = Age of the supplanted kid +increase in normal x number of terms

i.e. the age of the recently included kid = 13 + 2 x 6 = 25

Principle 7: There are two more situations when the arrangement is partitioned into two sections and one of the terms is either included or rejected, then the center term can be computed by taking after strategies.

सिद्धांत 7: दो और स्थितियों जब व्यवस्था को दो भागों में विभाजित है और शर्तों में से एक या तो शामिल किया जाता है या अस्वीकार कर रहे हैं, तो केंद्र अवधि की रणनीति के बाद लेने से गणना की जा सकती।

Example 1 : When the term is prohibited.

Average(total ) + number of terms in initial segment x {average (all out) – normal (first part)} + number of terms in second part x {average (absolute) – normal (second part)}

Example 2: When the term is incorporated.

Normal (aggregate) + number of terms in initial segment x {average (initial segment) – average(total) }+ x number of terms in second part x {average (second part) – normal (total)}

For Example: The normal of 20 numbers is 12 .The midpoints of the initial 12 is 11 and the normal of next 7 numbers is 10. The last number will be?

Arrangement:

Here for this situation one number is rejected so the number would be =

Average(total ) + number of terms in initial segment x {average (all out) – normal (first part)} + number of terms in second part x {average (complete) – normal (second part)} i.e. = 12 + 12 x (12-11)+(12-10) x 7 = 38.

 

 

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