Central tendency
Introduction to Statistics (Measures of Central Tendency) Central Tendency: In a representative sample, the value of a series of data have a tendency to cluster around a certain point usually at the center of the series is usually called central tendency and its numerical measures are called the measures of central tendency or measures of location.
Different Measures of Central Tendency: The following are the important measures of central tendency which are generally used in business:
Arithmetic mean
Geometric mean
Harmonic Mean
Median
Mode
Arithmetic mean: Arithmetic mean is defined as the sum of all observations divided by the total number of observations.
Calculation of Arithmetic Mean-Ungrouped Data: For ungrouped data, arithmetic mean may be computed by applying any of the following methods:
Direct method
Short-cut method
Direct method: The arithmetic mean, often simply referred to as mean, is the total of the values of a set of observations divided by their total number of observations. Thus, if represent the values of items or observations, the arithmetic mean denoted by is defined as:
If the subscripts are dropped, the formula sample mean is: = and the population mean is:
Short-cut method: According to short-cut method arithmetic mean can be computed by the formula:
, where , here A is called origin and h is called scale.
Example: The monthly expenditure (in taka) of 10 students given as follows:
14870 14930 15020 14460 14750 14920 15720 15160 14680 14890
Find monthly average expenditure.
Solution: Let income be denoted by X
By using calculator,
=149400
===14940
Hence, the average monthly income Tk.14940
Example: Mr. Peterson is studying the number of minutes used monthly by clients in a particular cell phone rate plan. Random sample of 12 clients showed the following number of minutes used last month.
90 77 94 89 119 112 91 110 92 100 113 83
What is the arithmetic mean number
Different Measures of Central Tendency: The following are the important measures of central tendency which are generally used in business:
Arithmetic mean
Geometric mean
Harmonic Mean
Median
Mode
Arithmetic mean: Arithmetic mean is defined as the sum of all observations divided by the total number of observations.
Calculation of Arithmetic Mean-Ungrouped Data: For ungrouped data, arithmetic mean may be computed by applying any of the following methods:
Direct method
Short-cut method
Direct method: The arithmetic mean, often simply referred to as mean, is the total of the values of a set of observations divided by their total number of observations. Thus, if represent the values of items or observations, the arithmetic mean denoted by is defined as:
If the subscripts are dropped, the formula sample mean is: = and the population mean is:
Short-cut method: According to short-cut method arithmetic mean can be computed by the formula:
, where , here A is called origin and h is called scale.
Example: The monthly expenditure (in taka) of 10 students given as follows:
14870 14930 15020 14460 14750 14920 15720 15160 14680 14890
Find monthly average expenditure.
Solution: Let income be denoted by X
By using calculator,
=149400
===14940
Hence, the average monthly income Tk.14940
Example: Mr. Peterson is studying the number of minutes used monthly by clients in a particular cell phone rate plan. Random sample of 12 clients showed the following number of minutes used last month.
90 77 94 89 119 112 91 110 92 100 113 83
What is the arithmetic mean number