PPT: Average

 Page 1


A v e r a g e s
Page 2


A v e r a g e s
What are Averages?
Definition
Averages can be defined as the central value in a set of data. They 
represent the middle value of a data set, providing a single figure that 
summarizes the entire collection.
Calculation
Average can be calculated simply by dividing the sum of all values in a 
set by the total number of values.
Applications
The data set can be of anything like age, money, runs in cricket, or any 
other numerical values that need to be represented by a central 
tendency.
Page 3


A v e r a g e s
What are Averages?
Definition
Averages can be defined as the central value in a set of data. They 
represent the middle value of a data set, providing a single figure that 
summarizes the entire collection.
Calculation
Average can be calculated simply by dividing the sum of all values in a 
set by the total number of values.
Applications
The data set can be of anything like age, money, runs in cricket, or any 
other numerical values that need to be represented by a central 
tendency.
Basic Formulae to 
Remember
1
Simple Average
Also known as Arithmetic Mean = (a ¡ + a ¢ + a £ &.a ¹) / n, where n is 
the number of values in the set.
2
Weighted Average
A type of average where each value has a specific weight or 
importance assigned to it.
3
Geometric Mean
Used when dealing with products or percentages, especially in 
finance and investment calculations.
4 Harmonic Mean
Particularly useful for rates and ratios, commonly used in calculating 
average speeds.
Page 4


A v e r a g e s
What are Averages?
Definition
Averages can be defined as the central value in a set of data. They 
represent the middle value of a data set, providing a single figure that 
summarizes the entire collection.
Calculation
Average can be calculated simply by dividing the sum of all values in a 
set by the total number of values.
Applications
The data set can be of anything like age, money, runs in cricket, or any 
other numerical values that need to be represented by a central 
tendency.
Basic Formulae to 
Remember
1
Simple Average
Also known as Arithmetic Mean = (a ¡ + a ¢ + a £ &.a ¹) / n, where n is 
the number of values in the set.
2
Weighted Average
A type of average where each value has a specific weight or 
importance assigned to it.
3
Geometric Mean
Used when dealing with products or percentages, especially in 
finance and investment calculations.
4 Harmonic Mean
Particularly useful for rates and ratios, commonly used in calculating 
average speeds.
Median and Mode
Median
The median of a finite list 
of numbers can be found 
by arranging all the 
observations from lowest 
value to highest value and 
picking the middle one. It's 
less affected by outliers 
compared to the mean.
Mode
The mode is the value that 
occurs most often in a 
data set. It can be 
calculated using the 
formula: Mode = 
3×Median - 2×Mean
Important Note
Sum of first n consecutive 
natural numbers = 
[n(n+1)]/2 Average of first 
n consecutive natural 
numbers = (n+1)/2
Page 5


A v e r a g e s
What are Averages?
Definition
Averages can be defined as the central value in a set of data. They 
represent the middle value of a data set, providing a single figure that 
summarizes the entire collection.
Calculation
Average can be calculated simply by dividing the sum of all values in a 
set by the total number of values.
Applications
The data set can be of anything like age, money, runs in cricket, or any 
other numerical values that need to be represented by a central 
tendency.
Basic Formulae to 
Remember
1
Simple Average
Also known as Arithmetic Mean = (a ¡ + a ¢ + a £ &.a ¹) / n, where n is 
the number of values in the set.
2
Weighted Average
A type of average where each value has a specific weight or 
importance assigned to it.
3
Geometric Mean
Used when dealing with products or percentages, especially in 
finance and investment calculations.
4 Harmonic Mean
Particularly useful for rates and ratios, commonly used in calculating 
average speeds.
Median and Mode
Median
The median of a finite list 
of numbers can be found 
by arranging all the 
observations from lowest 
value to highest value and 
picking the middle one. It's 
less affected by outliers 
compared to the mean.
Mode
The mode is the value that 
occurs most often in a 
data set. It can be 
calculated using the 
formula: Mode = 
3×Median - 2×Mean
Important Note
Sum of first n consecutive 
natural numbers = 
[n(n+1)]/2 Average of first 
n consecutive natural 
numbers = (n+1)/2
Important Points on Average Changes
1
Person Replacement
When a person replaces another: If average increases, Age of new person = Age of person who left + (Increase in 
average × total number of persons). If average decreases, Age of new person = Age of person who left - (Decrease in 
average × total number of persons).
2
Person Joining
When a person joins the group: In case of increase in average, Age of new member = Previous average + (Increase in 
average × Number of members including new member). In case of decrease, Age of new member = Previous average - 
(Decrease in average × Number of members including new member).
3
Arithmetic Progression
When the number of terms is odd - the average will be the middle term. When number of terms are even - the average 
will be the average of two middle terms.