SimpleMaths

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