PPT: Measures of Central Tendency

 Page 1


Measures of 
Central Tendency
Page 2


Measures of 
Central Tendency
INTRODUCTION
Consider Baiju, a farmer from Balapur village in Buxar, Bihar. To assess his economic 
standing among the village's 50 small farmers, we can determine if his land holding is 
above, below, or near the average land holding size in the village.
1
above average (see 
the Arithmetic Mean)
2
above what half the 
farmers own (see the 
Median)
3
above what most 
farmers own (see the 
Mode)
These three measures allow us to represent the entire dataset with single, representative 
values:
1
Arithmetic Mean
2
Median
3
Mode
Page 3


Measures of 
Central Tendency
INTRODUCTION
Consider Baiju, a farmer from Balapur village in Buxar, Bihar. To assess his economic 
standing among the village's 50 small farmers, we can determine if his land holding is 
above, below, or near the average land holding size in the village.
1
above average (see 
the Arithmetic Mean)
2
above what half the 
farmers own (see the 
Median)
3
above what most 
farmers own (see the 
Mode)
These three measures allow us to represent the entire dataset with single, representative 
values:
1
Arithmetic Mean
2
Median
3
Mode
ARITHMETIC MEAN
Consider six families with monthly incomes (in Rs): 1600, 1500, 1400, 1525, 1625, 1630.
The mean family income = (1600 + 1500 + 1400 + 1525 + 1625 + 1630)/6 = Rs 1,547
This indicates that, on average, a family earns Rs 1,547.
Arithmetic mean is the most common measure of central tendency.
It equals the sum of all values divided by the number of observations, denoted by X
 .
For N observations (X¡, X¢, X£, ..., X¹), the formula is:
X
 = (X¡ + X¢ + X£ + ... + X¹)/N = 3X/N
Where 3X represents the sum of all observations and N is the total number of observations.
Page 4


Measures of 
Central Tendency
INTRODUCTION
Consider Baiju, a farmer from Balapur village in Buxar, Bihar. To assess his economic 
standing among the village's 50 small farmers, we can determine if his land holding is 
above, below, or near the average land holding size in the village.
1
above average (see 
the Arithmetic Mean)
2
above what half the 
farmers own (see the 
Median)
3
above what most 
farmers own (see the 
Mode)
These three measures allow us to represent the entire dataset with single, representative 
values:
1
Arithmetic Mean
2
Median
3
Mode
ARITHMETIC MEAN
Consider six families with monthly incomes (in Rs): 1600, 1500, 1400, 1525, 1625, 1630.
The mean family income = (1600 + 1500 + 1400 + 1525 + 1625 + 1630)/6 = Rs 1,547
This indicates that, on average, a family earns Rs 1,547.
Arithmetic mean is the most common measure of central tendency.
It equals the sum of all values divided by the number of observations, denoted by X
 .
For N observations (X¡, X¢, X£, ..., X¹), the formula is:
X
 = (X¡ + X¢ + X£ + ... + X¹)/N = 3X/N
Where 3X represents the sum of all observations and N is the total number of observations.
How Arithmetic Mean is Calculated
Arithmetic Mean for Ungrouped Data
Methods for calculating arithmetic mean when data is not grouped into frequency 
distributions
Arithmetic Mean for Grouped Data
Methods for calculating arithmetic mean when data is organized into frequency 
distributions
Page 5


Measures of 
Central Tendency
INTRODUCTION
Consider Baiju, a farmer from Balapur village in Buxar, Bihar. To assess his economic 
standing among the village's 50 small farmers, we can determine if his land holding is 
above, below, or near the average land holding size in the village.
1
above average (see 
the Arithmetic Mean)
2
above what half the 
farmers own (see the 
Median)
3
above what most 
farmers own (see the 
Mode)
These three measures allow us to represent the entire dataset with single, representative 
values:
1
Arithmetic Mean
2
Median
3
Mode
ARITHMETIC MEAN
Consider six families with monthly incomes (in Rs): 1600, 1500, 1400, 1525, 1625, 1630.
The mean family income = (1600 + 1500 + 1400 + 1525 + 1625 + 1630)/6 = Rs 1,547
This indicates that, on average, a family earns Rs 1,547.
Arithmetic mean is the most common measure of central tendency.
It equals the sum of all values divided by the number of observations, denoted by X
 .
For N observations (X¡, X¢, X£, ..., X¹), the formula is:
X
 = (X¡ + X¢ + X£ + ... + X¹)/N = 3X/N
Where 3X represents the sum of all observations and N is the total number of observations.
How Arithmetic Mean is Calculated
Arithmetic Mean for Ungrouped Data
Methods for calculating arithmetic mean when data is not grouped into frequency 
distributions
Arithmetic Mean for Grouped Data
Methods for calculating arithmetic mean when data is organized into frequency 
distributions
Arithmetic Mean for Series of Ungrouped 
Data
Direct Method
Arithmetic mean by direct method is the sum of all observations in a series divided by the 
total number of observations.
Calculate Arithmetic Mean from the data showing marks of students in a class in an 
economics test: 40, 50, 55, 78, 58.
Formula: X
 = 3X/N
Calculation: X
 = (40 + 50 + 55 + 78 + 58)/5 = 281/5 = 56.2
The average mark of students in the economics test is 56.2.