SimpleMaths

Percentile : Percentile Definition : " All data divided into hundred equal parts is known as Percentile. " It is clear that the items which divided the data into hundred equal parts lie at the P1, P2, P3, ..., P100 the way down the arrangement. Percentile denoted by P1 means first Percentile, P2 means second Percentile, P3 means third Percentile and so on respectively.        Quartiles          Deciles          Mean                          Percentile Formulas : For Individual items and Discrete Distribution :   First Percentile = P1 = Size of [ ( N + 1 ) / 100 ]th item. Second Percentile = P2 =  Size of 2 × [ ( N + 1 ) / 100 ]th item --------- --------- --------- Hundredth Percentile = P100 = Size of ( N + 1 ) th item. For Continues Distribution : First  Percentile = P1 =Size of [N /100 ]th item. Second Percentile = P2 =  Size of 2 × [ N / 100 ]th item --------- --------- --------- Hundredth Percentile = P100 = Size of Nth item. Perc

Decile : Decile Definition : " All data divided Ten equal parts is known as Decile. " It is clear that the items which divided the data into ten equal parts lie at the D1, D2, ...., D10 of the way down the arrangement. Decile denoted by D1 means first decile, D2 means second decile, and so on D10 means tenth decile respectively.               Mean          Median         Quartiles Decile Formulas : For Individual items and Discrete Distribution : 1) First Decile = D1 = Size of [ ( N + 1 ) / 10 ]th item. 2) Second Decile = D2 =  Size of 2 × [ ( N + 1 ) / 10 ]th item. 3) Third Decile = D3 = Size of 3 × [ ( N + 1 ) / 10 ] th item. and so on, 10) Tenth Decile = D10 = Size of  ( N + 1 ) th item. For Continues Distribution : 1) First Decile = D1 = Size of [ N / 10 ]th item. 2) Second Decile = D2 = Size of 2 × [ N / 10] th item and so on, 10) Tenth Decile = D10 = Size N th item. Deciles Examples : Computation of Dec

Quartiles : Quartile Definition : " All data divided four equal parts is known as Quartile. " It is clear that the items which divided the data into four equal parts lie at the quarter, half and three quarters, of the way down the arrangement. Quartile denoted by Q1 means first quartile, Q2 means second quartile, Q3 means third quartile respectively. Clearly the second quartile is the Median item. Mean         Median          Mode Quartile Formulas : For Individual items and Discrete Distribution : 1) First Quartile = Q1 = Size of [ ( N + 1 ) / 4 ]th item. 2) Third Quartile = Q3 =  Size of 3 × [ ( N + 1 ) / 4 ]th item For Continues Distribution : 1)  First Quartile = Q1 = Size of [ N / 4 ]th item. 2) Third Quartile= Q3 =Size of 3 × [ N / 4 ] th item Quartiles Examples : Computation of Quartiles for Individual Data : 1) Calculate the first, second and third quartile from the following values weights in kg of a group of students. 50, 51

Various Dimensions : Dimensions : Different types of measurements are used to measure different objects, their length, size and mass. This is called dimension. Decimal dimension : Decimal method dimensions are used to measure length, mass and Volume of matter. Important things : 1. Meters are used to measure the length of an object as well as space. 2. Measures the distance between two places or villages in kilometers. 3. Liters are used to measure liquids like milk, water, oil, etc. 4. Kilograms are used to measure food and other items. 5. Seconds, minutes and hours are used to measure time. Length measurement : 1) 10 ml = 1 cm 2) 10 centimeters = 1 decimeter 3) 10 decimeters = 1 meter 1) 10 meters = 1 decimeter 2) 10 decimeters = 1 hectometer 3) 10 hectometers = 1 kilometer 1) 10 mg = 1 centigram 2) 10 centigram = 1 decigram 3) 10 decigrams = 1 gram 1) 10 Hectograms = 1 Kilograms 2) 100 kg = 1 quintal 3) 100 quintals = 1 t

Mode in statistics : Mode definition : For example, some data such as follows : 2, 1, 2, 5, 4, 2, 2, 7, 8, 2. Here, 2 value repeated 5 times that is repeated many times as compared another data. Therefore, 2 is Mode." It is straight forward to calculate mode in case of individual and discrete data.               Mean          Median         Quartile How do you find the mode of  Individual Data ? Que. 1) The following are the marks of 10 students. Calculate the mode. 60, 67, 76, 56, 77, 67, 48, 67, 89, 90. Ans. : Marks            : 48  56  60  67  76  77  89  90 Frequency   :  01  01  01  03  01  01  01  01 Here 67 mark repeated many times that is 3 times. therefore, Mode = 67. Que. 2)  The following are the height in cm of 12 students. Calculate the mode. 40, 41, 43, 41, 46, 47, 41, 41, 40, 42, 41,  46. Ans. : Heights         : 40  41  42  46  47 Frequency   :  02  05  01  03  01 Here 41 cm  height repeated many times that is 5 times. there

Median definition statistics : if the set contains an odd number of items, the middle item of an array is median . in array we arrange the data in ascending or descending order of magnitude. Median is a positional average. it indicates the value of the item positioned at the center. it is 50th percentile. the value below and above median is 50%.            Mean       Mode          Quartile How to find Median : Median formula : If data set contains an odd number of items then, Me = value of [ ( n + 1 ) / 2 ] th item. here, n = total frequency of distribution. If data set contains an even number of items then, there will be two items which stand at the center. therefore, Me = we may take the average of these two, as the median. Median based on Individual Data : Que. 1 : Calculate median for the following data. 24, 36, 9, 26, 78, 46, 4. Ans. : First we, Arrange the data in ascending order 4, 9, 24, 26, 36, 46, 78. here, n = 7 Me = Size of [ ( n + 1 ) / 2 ] th

Arithmetic mean : Arithmetic Mean Definition : " The arithmetic mean means sum of the given numbers divided by total numbers."               Mode         Median          Quartile Arithmetic Mean Formula : Arithmetic Mean = ( Sum of given numbers ) / Total numbers. X = ( a1 + a2 + a3 + ----- + an ) / N where, X = Arithmetic Mean, N = Total numbers. Arithmetic Mean Examples based on Individual data. : Que.1: Calculate mean of the following values. 24, 43, 34, 65, 78, 20. Ans. : Arithmetic Mean = ( Sum of given numbers ) / Total numbers. Arithmetic Mean = ( 24 + 43 + 34 + 65 + 78 + 20 ) / 6 Arithmetic Mean = 264 / 6 Arithmetic Mean = 44 Que. 2 : Calculate mean of the following values. 21, 25, 35, 40, 39. Ans. : Arithmetic Mean = ( Sum of given numbers ) / Total numbers. Arithmetic Mean  = ( 21 + 25 + 35 + 40 + 39 ) / 5 Arithmetic Mean  = 160 / 5 Arithmetic Mean  = 32. Que.3) The mean of a group of 7 observation is 12

Variation Introduction: Types of Variation : There are two types of variation such as follows : 1) Direct Variation 2) Inverse Variation. Examples of Direct Variation : 1) If 10 books cost Rs. 100, then what is the cost of 15 such books ? Ans. : Here, as the cost of book will increases with an increases in their number, we have a case of direct variation. x = Number of books = 10 y = Cost of 10 books = 100 therefore, x / y = 10 / 100 also, Number of books = 15 Suppose cost of 15 books = Rs. y In direct variation, the ratio of the number of books of the cost of books must be constant. therefore, 10 / 100 = 15 / y y = ( 100 × 15 ) / 10 y = 150 therefore, the cost of 15 books is Rs. 150 2) If the shadow of a 12 meter high building falls 9 meters then how many meters will the shadow of a 9 meter high building fall? Ans. : Suppose x = building height y = building of shadow x / y = 12 / 9 = 9 / y therefore, y = ( 9 × 9 ) / 12 y = 81 / 12 y = 6.75 meters Th

Linear equations in two variables : Definition of simultaneous equations : " Two equations that are considered at the same time are called simultaneous equations. " Solution of simultaneous equations : if each of the equations in a simultaneous equation is satisfied by a common value pair of variables then this pair of variables is called a solution of a simultaneous equation. Simultaneous equations examples : 1) x + y = 100      x - y = 20 So how many x and y. Solution : x + y = 100 -------- I x - y = 20 --------- II Adding equation I from equation II , we get 2x = 120 x = 120 / 2 x = 60 Let's put  x = 60 in equation I , we get 60 + y = 100 y = 100 - 60 y = 40 Therefore, values of x and y  is ( 60, 40 ) . By verification : The given solution should be kept in the equation. If both the values   are the same then it should be considered as a solution. Above two simultaneous equations are x + y = 100 and x - y = 20 put x = 60 and y = 40 in

What is Linear equation : Important things to remember : 1) Real numbers a and b (where a is not equal to zero) and x is a variable, So the equation ax + b = 0 is called one variable linear equation. 2) The left hand side of the equation ax + b = 0 is a linear polynomial and there is only one variable in that polynomial. 3) If a given equation converts to an equation of the form ax + b = 0, then it is said to be a linear equation in one variable. 4)The exponent of the x variable in the equation is one. These equations are like the general form of the linear equation ax + b = 0. So they are linear equations. Linear equation example : 1) 5x - 12 = 0 2) 7x + 6 = 9x - 4 3) x + 9 = 4x. Solve the equation : 1) The number by which both sides of the equation are equal in value. That number is said to satisfy the equation. 2) The number that satisfies the equation is called the solution of the equation. 3) The set of solutions of an equation is the set of solutions of tha

Single equation method :  An equation has a single variable, that equation is called a single variable. If the variable exponent of a variable equation is 1, then that equation is called a simple equation. Example : a + 7 = 18 The value at which the variable satisfies the equation is called a unitary equation. Examples of single equation : 1)  3a + 4 = 10             3a = 10 - 4             3a = 6             a = 6 / 3             a = 2 2) 4a + 1 = 9            4a = 9 - 1            4a = 8            a = 8 / 4            a = 2 3) 3b - 5 = 4           3b = 4 + 5           3b = 9           b = 9 / 3           b = 3 4) ( b / 110) - 60 = 240          ( b / 110 ) = 240  + 60          ( b / 110 ) = 300           b = 300 × 110           b = 33000 5) ( b / 40) + 60 = 70           ( b / 40 ) = 70 - 60           ( b / 40 ) = 10            b = 10 × 40            b = 400 6) 5a - 8 = 2 ( a - 1 )          5a - 8 = 2a - 2          5a - 2a = 8 - 2          3a = 6

What is Partnership: In a trade, sometimes two or more partners invest their capital together and divide the profit or loss in that trade into the amount invested. If the capital invested in a trade is for different periods, then the division of profit or loss is in proportion to the multiplication of capital and term. Properties of partnership : 1. The amount invested to set up a trade or industry is called capital. 2. People who participate in a transaction are called partners. 3. The transaction of the partner is called partnership. 4. If the trading partners have the same term, the profit or loss share is equal to the capital. 5. A partnership of equal duration is called a simple partnership. 6. If the trading partners have different capital and term, the distribution of profit or loss is equal to the product of capital and term. 7. Trade partnership if the profit or loss is the same, There is an inverse ratio between the capital ratio and the term ratio.