GURU HARKRISHAN PUBLIC SCHOOL SENIOR CAMPUS SRI GANGANAGAR

GURU HARKRISHAN PUBLIC SCHOOL (SENIOR CAMPUS) SRI GANGANAGAR 2020 -21 GHPS CONNECTS CLASS - XI Subject – Applied Mathematics (241) Meenu Rana ghpsonline@gmail. com meenurana 8696@gmail. com

AVERAGE “A number expressing the central or typical value in a set of data” which is calculated by dividing the sum of the values in the set by their number. Also called the Arithmetic Mean

Exp 1: What is the average of 2, 7 and 9? Sol: Add the numbers: 2 + 7 + 9 = 18 Divide by how many numbers (i. e. we added 3 numbers): 18 ÷ 3 = 6 So the average is 6

Quick Tips and Tricks: Average of first “n”whole numbers = Exp 2: Find the average of first ten whole numbers. Sol: Average of first “ n” whole numbers = n=10 According to above formula = (10 - 1) / 2 = 4. 5

Average of first “n”natural numbers = Exp 3: Find the average of the first 97 natural numbers. Sol: Average of first ” n” natural numbers = n = 97 According the formula (97 + 1) / 2 = 49

Average of first “n” multiple of “m” = Exp 4: Find the average of first 10 multiples of 12 Sol: Average of first “n” multiple of “m” = n= 10 and m = 12 According the formula = 12 ( 10+1) / 2 = 6 x 11 = 66.

Average of n odd numbers = n Exp 5: Calculate the average of first 5 odd numbers. Sol: Average of n odd numbers = n n=5 , so Average = 5 Other way : first 5 odd no’s = 1, 3, 5, 7, 9 Average= (1+3+5+7+9) / 5 =25/5 = 5

Average of n even numbers = n + 1 Exp 6: Calculate the average of first 6 even numbers. Sol: Average of n even numbers = n+1 n=6 , so Average = 6+1 =7 Other way : first 6 even no’s = 2, 4, 6, 8, 10, 12 Average= (2+4+6+8+10+12) / 6 =42/6 = 7

TRY : Average of squares of first 'n' natural numbers=(n+1)(2 n+1) 6 Average of cubes of first 'n' natural numbers=n(n+1)2 4

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