Question

Average Tutorials & Tricks

Answer 1

Introduction
This lesson introduces the concepts of mean, median, and mode as they are used in statistics to measure the central tendency of collections of data.

Formulae & Examples
Formula for finding out Average.
Rule : Average = Sum of data / No. of data

1. Average = sum of quantities/number of quantities

2. Sum = avg * no. of quantities

3. If the numbers are in A.P. (Arithmetic Progression), then the avg of numbers is given by
    Avg = sum/n =[ (n/2)(a+l)]/n
                    = (a+l)/2
    Where  n – no. of quantities
                    a – first term or value
                    l – last term or value

4. Weighted Average:
    Section1:
                    No. of quantities: m
                    Avg of section1: p
    Section2:
                    No. of quantities: n
                    Avg of section1: q
    Avg of section1 and section2 = (m*p + n*q)/(m +n)


Points to remember/Shortcuts
1. Average lies between minimum and maximum values.
a. Avg > minimum value
b. Avg < maximum value
2. If every quantity is increased/decreased by ‘k’ value, then the avg also get increased/decreased by the same ‘k’ value.

                        
Sample Example
Ex
The average of 13 results is 40 and that of first six is 30 and last six is 34. Find the value of 7 th number ?
A7 th
number will be = Sum of 13 results - ( Sum of first six + Sum of last six ) = ( 13 * 40 ) - ( 6 * 30 + 6 * 34 ) = 136.
Ex
In a class, there are 20 students whose average age is decreased by two months, when one student aged 18 years is replaced by a new student, find the age of the new student ?
A
Age of new student = Age of removed student - Numbers of students * Decrease in average age = 18 - 20 * ( 2 / 12 ) = 44 / 3 = 14 years 8 months.
Ex
A man divides his total journey into three equal parts and decides to travel the three parts with speeds 60 km / hr , 24 km / hr and 45 km /hr . Find the average speed during the whole journey ?
A
speed = 3 * 60 * 24 * 45 / 60 * 24 + 24 * 45 + 45 * 60 = 37.24 km / hr.
Ex
The mean temperature of Monday to Wednesday was 27 °C and of Tuesday to Thrusday was 24 °C. If the temperature on Thrusday was 2 / 3 rd of the temperature on Monday, What was the temperature on Thrusday ?
A
Mon + Tue + Wed = 81
Tue + Wed + Thu = 72
hence    Mon - Thu = 9
Also Thu = ( 2 /3 ) * Mon

So the temperature of Thrusday = 18 °C
Ex
A batsman makes a score of 70 runs in the 15 th inning and thus increases average by 2 runs. Find the average after 15 th inning ?
A
Let the average after 15 th inning be x

The average after 14 th inning = (x-2)

Now 14 (x-2)+70=15x

So x=42