Skip to main content

average formula

To find the average, first we need to calculate the sum of the elements, then we have to divide the sum of the elements by the no of elements to get the average.
                                               Average= sum of elements/ no of elements

               Ex:         The average of first 5 natural numbers
                                 sum of 5 natural numbers=1+2+3+4+5=15
                                 no of elements = 5
                                 average = 15/5 =3
                                       

Comments

Popular posts from this blog

average of first 100 odd numbers

  Odd  numbers are 1,3,5,7,9,…. Average = sum of elements/  no  of elments Now we will see the sum of elements: Sum of first 2 odd  numbers: 1+3= 4= 2 2 Sum of first 3 odd  numbers: 1+3+5= 9= 3 2 Sum of first 4 odd  numbers: 1+3+5+7=16= 4 2 Sum of first 5 odd  numbers: 1+3+5+7+9 = 25 = 5 2 Sum of first n odd  numbers: 1+3+5+7+9+. . . . .  n numbers= n 2 Now we will see average: Average of first 2 odd numbers= (1+3)/2                                                           = 4/2                                                                 =2 Average of first 3 odd  numbers= (1+3+5)/3                                                           = 9/3                                                                 =3 Average of first 4 odd  numbers= (1+3+5+7)/4                                                           = 16/4                                                                 =4 Average of first 5 odd numbers= (1+3+5+7+9)/5            

LOGIC BEHIND MAGIC SQUARE

Assume a magic square of 3x3 A B C D E F G H I The above figure shows a 3x3 magic square. In the magic square sum of colum, row, diagnol numbers should be same A+B+C=D+E+F=G+H+I=A+D+G=B+E+H=C+F+I=A+E+I=C+E+G=sum A+B+C D+E+F G+H+I A+D+G B+E+H C+F+I A+E+I C+E+G By  seeing the  above there is 8 type of sum is available. Row wise-3,  column wise-3, diagnol wise-2. Condition#1: There are 8 different combinations are there with same sum in a magic square. In the above 8 combinations A=2 times, B= 3 times, C= 2 times, D=3 times E=4 times, F=3 times, G=2 times, H=3 times, I= 2 times Hence the above forms the condition#2. In simply condition#2, middle number E appears 4 times in 8 combinations. Hence row, column, diagnol sum should be equal. In 3x3 magic square we are taking numbers from 1 to 9. From 9 numbers we need to take 3 numbers. From combination f

average of first n natural numbers

The natural numbers are 1,2,3,4,5,. . . . . . now we will see the sum of natural numbers                       sum of first 3 natural numbers= 1+2+3=6 the above can be written as                      sum of first 3 natural numbers= 1+2+3=6=3(3+1)/2                      sum of first 4 natural numbers= 1+2+3+4=4(4+1)/2                      then sum of n natural numbers=1+2+3+......n terms=n(n+1)/2 then the average formula = sum of elements/no of elements                     the average of n natural numbers= sum of elements/ no of elements                                                                         =(n(n+1)/2)/n                                                                         =n(n+1)/2xn                                                                         =(n+1)/2   THE AVERAGE OF FIRST N NATURAL  NUMBERS=(n+1)/2 The average of first 5 natural numbers                                  sum of 5 natural numbers=1+2+3+4+5=15