Aptitude - AVERAGE

AVERAGE

This is the effort of The Boss Academy to provide high quality study materials & model question papers for all competitive Nursing exams. Utilize our small effort & share to others to brighten Nursing profession. And we welcome your most valuable suggestions to improve our services & help us to do it best way to spread knowledge, skills & power.

Mathematically,

Arithmetic Mean= average = Sum of terms/ No. of terms.

Properties of average

•The average of the first and last term would also be the average of all the terms of the sequence.

Ex. 4,5,6,7,8 . Average = 4+8/2=12/2=6.
Also 4+5+6+7+8/5=30/5=6

•In consecutive number sequence the middle term is the average. 

Ex . 11,12,13,14,15,16,17. Average is 14,
Also 11+12+13+14+15+16+17/7=98/7=14

•In case of odd number of terms with same difference, the average will be the middle term.

Ex. 1,3,5,7,9,11,13. Average is 7,
Also 1+3+5+7+9+11+13/7=49/7=7 

•In case of even number of terms with same difference, the average will be the average of two middle terms.

Ex. 82,84,86,88,90. Average is 86,
Also 82+84+86+88+90/5=430/5=86 

•If x is added to all the items, then the average increases by x.

•If x is subtracted from all the items, then the average decreases by x. 

•If every item is multiplied by x, then the average also gets multiplied by x. 

•If every item is divided by x, then the average also gets divided by x. 

•If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, 

then the combined average =n1X + n2Y/n1+n2 

•If the average of group of n1 quantities is x and the average of n2 quantities out of them is y, 

the average of the remaining group = n1X – n2Y/n 1 – n2 

•The average of first n natural numbers = (n+1)/2 

•The average of squares of first n natural numbers = (n+1)(2n+1)/6 

•The average of cubes of first n natural numbers = n(n+1)2/4 

•The average of odd numbers from 1 to n = (last odd number+1)/2 

•The average of even numbers from 1 to n = (last even 

number+2)/2 

•The average of squares of first n odd numbers = (2n+1)(2n-1)/3 

•The average of first n odd numbers = n2 

•A man covers a certain distance at x kmph and an equal distance at y kmph. Then the average speed during the whole journey is (2xy/x+y)kmph
Examples:

Q1). The body weight of six boys is recorded as 54kg, 75kg, 64kg, 67kg, 45kg, and 91kg. What is the average weight of the all six boys?

Ans 66 kg

Q2). There are six numbers 30, 72, 53, 68, x, 87, out of which x is unknown. The average of the numbers is 60. what is the value of x

Ans 50

Q3). The average marks scored by 35 students of a class is 50. if one student is left out, the average falls to 49. Marks of that left student ?

Ans 84

Q4). Average weight of 40 students in a class is 42 kg. if the class teacher’s weight is included, then the average is increased by one, then weight of the teacher is ?

Ans 83

Q5). The mean marks of 50 students was found to be 45, later on it was found a score of 43 was misread as 73, then the correct mean is

Ans 44.4

Q6). Average marks obtained by 20 students is 45. The average of first ten is 50 & of last 9 is 40. what are the marks obtained by the 11th student?

Ans 40

Q7). The average age of a class of 40 students is 15 years. Ram & Lakshman, who are twins, came to the class, but the average age of the class not changed. Find ram’s age ?

Ans 15

Above questions are explained in the following video

Click here for Explanation video link

Thanks

Visit our sites for more updates

www.thebossacadmy.net for study materials, model previous year question papers, books & journals

www.medjobss.com for all medical related professional Government jobs, notification, application &  apply online links.