Definitions [1]
Define the mean.
The mean is the value that is derived by summing all the values and dividing it by the number of observations.
`bar"x" = "Sum of observations"/"No. of observations"`
Formulae [3]
-
For Individual or Ungrouped Data
\[\mathrm{Q}_i=\text{size of }i\left(\frac{n+1}{4}\right)^\text{th Observation.}\quad i=1,2,3\]
-
For Grouped/Continuous Data
\[\mathbf{Q}_i=l+\left(\frac{\frac{in}{4}-cf}{f}\right)\times h\quad i=1,2,3\]
Where
l = Lower limit of quartile class.
f = Frequency of the quartile class
cf = Cumulative frequency of the class preceding the quartile class.
n = Total of frequency.
h = Upper limit - lower limit of the quartile class.
1. For Individual or Discrete Data:
\[\mathrm{D}_j=j\left(\frac{n+1}{10}\right)^\text{th Observation}\mathrm{~where~}j=1,2...9\]
2. For Grouped (Continuous) Data:
\[\mathbf{D}_j=l+\left(\frac{\frac{jn}{10}-cf}{f}\right)\times h,\quad j=1,2...9\]
Where
D = Decile
l = Lower limit of decile class
f = Frequency of decile class
cf = Cumulative frequency of class preceding decile class
h = Upper limit of the class – lower limit of the decile class.
A. For Individual or Discrete Data
Formula:
\[\mathrm{P}_k=\mathrm{size~of}k\left(\frac{n+1}{100}\right)^\text{th Observation}\] k = 1, 2,... 99
Where:
- k = Percentile number (1 to 99)
- n = Total number of observations
B. For Grouped/Continuous Data
Formula:
\[\mathbf{P}_k=l+\left(\frac{\frac{kn}{100}-cf}{f}\right)\times h\] k = 1, 2,... 99
Where
P = Percentile
l = Lower limit of percentile class
f = Frequency of percentile class
cf = Cumulative frequency of class preceding percentile class
h = Upper limit of the class – lower limit of the percentile class.
Key Points
- Given by Hermann Paasche
- Uses current year quantities as weights
- Measures price change
- Formula: (Σp₁q₁ / Σp₀q₁) × 100
- Example result: 212.69
Concepts [28]
- Measures of Central Tendency for Different Data Types
- Measures of Central Tendency - Central Value Or Representative Value
- Measures of Central Tendency - Series
- Quartiles
- Deciles
- Percentiles
- Measures of Dispersion - Absolute Dispersion
- Measures of Dispersion - Relative Dispersion
- Lorenz Curve
- Lorenz Curve
- Correlation Meaning
- Properties of Correlation,
- Types of Correlation
- Scatter Diagram of Correlation
- Measures of Correlation - Karl Pearson'S Method (Two Variables Ungrouped Data)
- Measures of Correlation - Spearman's Rank Correlation
- Uses of Index Numbers
- Types of Index Number - Wholesale Price Index
- Types of Index Number - Consumer Price Index
- Types of Index Number - Index of Industrial Production
- Construction of Price Index
- Cost of Living Index Number
- Inflation and Index Numbers
- Method to Measure - Simple Aggregate Method
- Method to Measure - Simple Average Price Relative Method
- Method to Measure - Laspeyer Method
- Paasche’s Price Index Number
- Method to Measure - Fisher's Method
