Table of contents  
Introduction  
Definition  
Weighted Mean  
Real Facts About Average  
Average Speed  
Instructions for the next 3 questions: 
Simple Average (or Mean) is defined as the ratio of the sum of the quantities to the number of quantities.
Here x_{1}, x_{2}, x_{3},  x_{n} represent the n values of a quantity under consideration & is the mean. Average or mean is said to be a measure of central tendency.
Example:
Average Formula
Let us take a very simple example of the first five natural numbers 1, 2, 3, 4 & 5:
Now let’s add 2 more 3’s to these 5 numbers:
Example 1. If a person with age 45 joins a group of 5 persons with an average age of 39 years. What will be the new average age of the group?
 Total age will be 45 + 5× 39 = 240. And there will be 6 persons now.
So, the average will be 240/6 = 40.
(or)Since, 45 is 6 more than 39, by joining the new person, the total will increase by 6 and so the average will increase by 1.
So, the average is 39 + 1 = 40.
Example 2. Two students with marks 50 and 54 leave class VIII A and move to class VIII B. As a result, the average marks of class VIII A fall from 48 to 46. How many students were there initially in class VIII A?
 The average of all the students of class VIII A is 46, excluding these two students.
 They have 4 and 8 marks more than 46. So, with the addition of these two students, 12 marks are adding more, and hence the average is increasing 2.
 There should be 6 students in that class, including these two. This is the initial number of students.
Example 3. The average of x successive natural numbers is N. If the next natural number is included in the group, the average increases by:
(a) Depends on x
(b) Depends on the starting number of the series
(c) Both (1) and (2)
(d)
(e) None of these
Correct Answer is Option (d)
The average of consecutive numbers is the middle number. If one more number is added to the list, the middle number moves 0.5 towards the right. So the answer is (d).
Example 4. The average marks of 30 students in a section of class X are 20 while that of 20 students of the second section is 30. Find the average marks for the entire class X.
We can do the question by using both the Simple average & weighted average method.
Average Speed Formula
Tip: Average Speed can never be double or more than double of any of the two speeds.
Example 5. The average of 10 consecutive numbers starting from 21 is:
The average is simply the middle number, which is the average of 5^{th} & 6^{th }no. i.e, 25 & 26 i.e. 25.5
There are 60 students in a class. These students are divided into three groups A, B, C of 15, 20 & 25 students each. The groups A & C are combined to form group D.
207 videos156 docs192 tests

1. What is the definition of weighted mean? 
2. What are some real facts about averages? 
3. What is average speed? 
4. How can I calculate the weighted mean? 
5. What are some instructions for calculating average speed? 
207 videos156 docs192 tests


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