TOPIC INFO (UGC NET)
TOPIC INFO – UGC NET (Economics)
SUB-TOPIC INFO – Statistics and Econometrics (UNIT 3)
CONTENT TYPE – Detailed Notes
What’s Inside the Chapter? (After Subscription)
1. Introduction
2. Measures of Central Tendency
2.1. Arithmetic Mean
2.2. Median
2.3. Mode
2.4. Relationship Between Mean, Median, and Mode
2.5. Other Measures: Geometric Mean and Harmonic Mean
3. Measures of Dispersion
3.1. Range
3.2. Quartile Deviation
3.3. Mean Deviation
3.4. Standard Deviation and Variance
3.5. Combined Standard Deviation
4. Correlation
4.1. Types of Correlation
4.2. Karl Pearson’s Coefficient of Correlation
4.3. Spearman’s Rank Correlation Coefficient
4.4. Coefficient of Determination
5. Index Numbers
5.1. Types of Index Numbers
5.2. Construction of Simple and Weighted Index Numbers
5.3. Laspeyres’ Price Index
5.4. Paasche’s Price Index
5.5. Fisher’s Ideal Index
5.6. Tests of Adequacy of Index Numbers
5.7. Uses and Limitations of Index Numbers
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Descriptive Statistics: Measures of Central Tendency & Dispersions, Correlation, Index Numbers
UGC NET ECONOMICS
Statistics and Econometrics (UNIT 3)
Introduction
Descriptive statistics refers to the branch of statistics concerned with the collection, organization, summarization, and presentation of data in a meaningful and informative manner, without drawing inferences beyond the data at hand. It is distinguished from inferential statistics, which uses sample data to make generalizations about a population. Descriptive statistics is fundamental to economic analysis because raw economic data—whether on prices, incomes, production, or trade—must be condensed into meaningful summary measures before any economic interpretation or policy conclusion can be drawn. The three principal tools of descriptive statistics discussed here are measures of central tendency, measures of dispersion, correlation, and index numbers.
Measures of Central Tendency
Measures of central tendency are summary statistics that represent the center point or typical value of a dataset, providing a single representative value around which the data tends to cluster. The three most important measures are the arithmetic mean, the median, and the mode.
Arithmetic Mean
The arithmetic mean is the most widely used measure of central tendency, calculated by summing all observations and dividing by the number of observations. For ungrouped data, the arithmetic mean is given by:
$$\bar{X} = \frac{\sum_{i=1}^{n} X_i}{n}$$
For grouped data (data organized in a frequency distribution), the arithmetic mean is calculated as:
$$\bar{X} = \frac{\sum f_i X_i}{\sum f_i}$$
where \(f_i\) is the frequency of the (i)-th class and \(X_i\) is the midpoint of that class. A shortcut method, the step deviation method, is also used for grouped data:
$$\bar{X} = A + \frac{\sum f_i d_i}{\sum f_i} \times h$$
where (A) is the assumed mean, \(d_i = \frac{X_i – A}{h}\), and (h) is the class width.
The arithmetic mean has several important mathematical properties: the sum of deviations of observations from the mean is always zero \((\sum (X_i – \bar{X}) = 0)\), and it is based on all observations, making it sensitive to extreme values (outliers). There is also the concept of weighted arithmetic mean, used when different observations carry different levels of importance:
$$\bar{X}_w = \frac{\sum w_i X_i}{\sum w_i}$$
where \(w_i\) represents the weight assigned to each observation. This concept is particularly important in economics for the construction of index numbers and computing average growth rates across sectors of differing sizes.
Example: If the monthly incomes (in ₹’000) of five households are 20, 25, 30, 35, and 40, the arithmetic mean is \(\bar{X} = \frac{20+25+30+35+40}{5} = 30\).