PPT: Average | Quantitative Techniques for CLAT PDF Download

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A v e r a g e s
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A v e r a g e s
I n t r o d u c t i o n
Averages can be defined as the central value in a set of data. Average can be calculated simply by 
dividing the sum of all values in a set by the total number of values. In other words, an average 
value represent the middle value of a data set. Average i.e. mean =
Example: What is the average of first five consecutive odd numbers?
Solution: The first five consecutive odd numbers are: 1, 3, 5, 7, 9. Here, the number of data or 
observations is 5 and the sum of these 5 numbers is 25. So, average = 25 / 5 = 5.
Page 3


A v e r a g e s
I n t r o d u c t i o n
Averages can be defined as the central value in a set of data. Average can be calculated simply by 
dividing the sum of all values in a set by the total number of values. In other words, an average 
value represent the middle value of a data set. Average i.e. mean =
Example: What is the average of first five consecutive odd numbers?
Solution: The first five consecutive odd numbers are: 1, 3, 5, 7, 9. Here, the number of data or 
observations is 5 and the sum of these 5 numbers is 25. So, average = 25 / 5 = 5.
Properties of Average
Property 1
The average always falls between the 
smallest and largest values in a dataset.
Property 2
In equally spaced numbers, the middle 
value (when arranged in order) equals 
the average.
Property 3
The sum of deviations below the average 
equals the sum of deviations above the 
average.
Property 4
Formula for calculating Average
Page 4


A v e r a g e s
I n t r o d u c t i o n
Averages can be defined as the central value in a set of data. Average can be calculated simply by 
dividing the sum of all values in a set by the total number of values. In other words, an average 
value represent the middle value of a data set. Average i.e. mean =
Example: What is the average of first five consecutive odd numbers?
Solution: The first five consecutive odd numbers are: 1, 3, 5, 7, 9. Here, the number of data or 
observations is 5 and the sum of these 5 numbers is 25. So, average = 25 / 5 = 5.
Properties of Average
Property 1
The average always falls between the 
smallest and largest values in a dataset.
Property 2
In equally spaced numbers, the middle 
value (when arranged in order) equals 
the average.
Property 3
The sum of deviations below the average 
equals the sum of deviations above the 
average.
Property 4
Formula for calculating Average
Important Formulae
Arithmetic Mean
Sum of all values / Number 
of values
Weighted Average
Sum of (Value × Weight) / 
Sum of Weights
Moving Average
Average of subset of data 
points over a specific 
period
Page 5


A v e r a g e s
I n t r o d u c t i o n
Averages can be defined as the central value in a set of data. Average can be calculated simply by 
dividing the sum of all values in a set by the total number of values. In other words, an average 
value represent the middle value of a data set. Average i.e. mean =
Example: What is the average of first five consecutive odd numbers?
Solution: The first five consecutive odd numbers are: 1, 3, 5, 7, 9. Here, the number of data or 
observations is 5 and the sum of these 5 numbers is 25. So, average = 25 / 5 = 5.
Properties of Average
Property 1
The average always falls between the 
smallest and largest values in a dataset.
Property 2
In equally spaced numbers, the middle 
value (when arranged in order) equals 
the average.
Property 3
The sum of deviations below the average 
equals the sum of deviations above the 
average.
Property 4
Formula for calculating Average
Important Formulae
Arithmetic Mean
Sum of all values / Number 
of values
Weighted Average
Sum of (Value × Weight) / 
Sum of Weights
Moving Average
Average of subset of data 
points over a specific 
period
Shortcuts
Calculating the Combined Average
To find the combined average of two data sets A and B, use this formula:
(N1 * X1 + N2 * X2) / (N1 + N2)
Where:
N1 = number of observations in set A
N2 = number of observations in set B
X1 = average of set A
X2 = average of set B