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Arithmetic Mean with Practical Examples, Study notes of Economics

Economics

A statistical tool is a method used to collect, organize, analyze, and interpret data for better decision-making. In economics, statistical tools help measure trends in income, production, prices, employment, and national growth. One important statistical tool is the arithmetic mean. The arithmetic mean, also called the average, shows the central value of a dataset.

Typology: Study notes

2025/2026

Available from 02/19/2026

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Statistical tools and interpretation
Statistical tools are methods or techniques which are used to collect,
organise, analyse and interpret the data.
Statistical tools
Measure Of Central Tendency
It refers to all those methods of statistical analysis which helps in determining
the averages of statistical series.
Measures of
Central Tendency
Correlation
Index Numbers
Measure Of
Central
Tendency
Airthmetic
Mean Median Mode
pf3
pf4
pf5
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pf9

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Download Arithmetic Mean with Practical Examples and more Study notes Economics in PDF only on Docsity!

Statistical tools and interpretation Statistical tools are methods or techniques which are used to collect, organise, analyse and interpret the data. Statistical tools Measure Of Central Tendency It refers to all those methods of statistical analysis which helps in determining the averages of statistical series.

Measures of

Central Tendency

Correlation

Index Numbers

Measure Of

Central

Tendency

Airthmetic

Mean

Median Mode

Airthmetic Mean ( Xˉ^ )

  • The sum of a series of numbers divided by the count of that series of numbers is the simple average or called as Arithmetic Mean. - Simple Arithmetic Mean - Weighted Arithmetic Mean
  • Methods/Calculations of Simple Arithmetic Mean For Ungrouped Data : Ungrouped data is a type of data that has not been organized or grouped into specific categories. It is also known as raw data or unorganized data.
  • By Direct Method
  • Xˉ^ = ΣX N where,ΣX = Total value of Items
  • N = Total number of items For Example : Score in Exams by students: 55, 67, 75, 69, 45, 88. Solution: ΣX= N= 6 Xˉ^ = 399 6

The arithmetic mean of the data set using the Simple method is 66.5.

  • By Assumed Mean Method
  • By Step Deviation Method
    • Xˉ^ = A + Σd’ N

× C

  • where, A = Assumed Mean
  • d’ = X-A C
  • C = Common factor
  • N = Number of observations For Example : Score in Exams by students: 5 0 , 55 , 60 , 65 , 70. Solution: Let’s take A= 60 C= d’= 300 - 60 5

Xˉ^ = 60 +

0 5

× 5 = 60

The arithmetic mean of the data set using the Step Deviation method is 60. For Grouped Data: Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

  • By Direct Method
    • Xˉ^ = Σ𝑓𝑋 Σ𝑓
  • where, ∑fX = Sum of product of frequency and X
  • ∑f = Sum of frequencies For Example: Class Interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency (f i ) 9 13 8 15 10 Solution: Class Interval Frequency (f i ) X fX 0 - 10 9 5 45 10 - 20 13 15 195 20 - 30 8 25 200 30 - 40 15 35 525 40 - 50 10 45 450 ∑f=55 ∑fX= Xˉ^ = 1415 55

The arithmetic mean of the data set using the Direct method is 25.73.

Xˉ^ = 25 +

40 55 = 25 + 0. = 25. The arithmetic mean of the data set using the Assumed Mean method is 25.73.

  • By Step Devation Method
    • Xˉ^ = A + Σ𝑓𝑑′ Σ𝑓

× C

  • where, A = Assumed Mean
  • d’ = X - A C
  • C = Class interval
  • ∑f = Sum of frequencies
  • For Example: Class Interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency (f i ) 9 13 8 15 10
  • Solution:

Class Interval Frequency (f i ) X d=X-A d’ fd’ 0 - 10 9 5 - 20 - 2 - 18 10 - 20 13 15 - 10 - 1 - 13 20 - 30 8 25 (A) 0 0 0 30 - 40 15 35 10 1 15 40 - 50 10 45 20 2 20 ∑f=55 ∑fX= 4 Let’s A= 25 C= 10 Xˉ^ = 25 + 4 55

× 10

The arithmetic mean of the data set using the Step Deviation method is 25.73.

Method/Calculation of Weighted Arithmetic Mean

A weighted average is the average of all the values which are arranged on a priority basis. The weighted average of values is the sum of the weight times values divided by the sum of the weights.

  • Xˉ^ 𝑤 = ΣWX ΣW
  • where,
  • ∑W = Total of weights
  • ∑WX = Total of Product of weights & items