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This chapter explains the importance of collecting data, the types of data sources, and methods of data collection.
Collection of Data – Formula & Equation Sheet
Essential formulas and equations from Statistics for Economics, tailored for Class 11 in Economics.
This one-pager compiles key formulas and equations from the Collection of Data chapter of Statistics for Economics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Mean (Average): μ = ΣX / N
μ is the population mean, ΣX is the sum of all observations, and N is the total number of observations. This formula calculates the central tendency of a dataset.
Median: If N is odd, Median = X[(N + 1)/2]; If N is even, Median = (X[N/2] + X[N/2 + 1]) / 2
The median divides the dataset into two equal parts. N is the number of observations, X represents the sorted data values.
Mode: Value that appears most frequently in a dataset.
The mode is useful for identifying the most common value in categorical data.
Standard Deviation: σ = √(Σ(X - μ)² / N)
σ represents the population standard deviation, X is each observation, μ is the mean, and N is the number of observations. This measures the dispersion of values in a dataset.
Variance: σ² = Σ(X - μ)² / N
Variance quantifies how much the values in a dataset differ from the mean. It is the square of the standard deviation.
Range: Range = Maximum value - Minimum value
The range gives the spread of data points in a dataset, providing quick insight into variability.
Sampling Error: SE = (Population Mean - Sample Mean)
SE represents the error in using a sample mean to estimate the population mean. Reducing SE often requires increasing sample size.
Non-Response Rate: Non-Response Rate = (Number of Non-responses / Total Sample Size) × 100
This measures the percentage of respondents who did not participate in a survey, indicating potential bias in data collection.
Census: C = Total Population
Census represents a method of collecting data from every member of a population, providing complete demographic information.
Sample Size (n): n = (Z² * p * (1-p)) / E²
Where Z is the Z-value for a confidence level, p is the estimated proportion, and E is the margin of error. This formula helps determine the adequate sample size for studies.
Equations
Primary Data Collection: Questionnaires & Surveys
This involves gathering first-hand data directly from respondents through structured forms.
Secondary Data: Derived from reports and previous studies.
Secondary data is collected by others. It is cheaper and quicker but may be less precise.
Random Sampling Formula: P(A) = Number of favorable outcomes / Total number of outcomes
P(A) represents the probability of selecting a specific sample, ensuring each individual in the population has an equal chance.
Systematic Sampling: Sample size = Population size / Desirable sample size
This method involves selecting random samples at a fixed interval from a randomly ordered list.
Stratified Sampling: n = (N * (Population Proportion))
In stratified sampling, n represents the sample size from a particular stratum based on its proportion in the population.
Census Data Equation: Total Population = Sum of All Households
This definition explains how total population is determined in census operations.
Exit Poll Formula: Predicted Winner = (Number of Votes for Candidate A) / (Total Votes)
This formula calculates the likelihood of a candidate winning based on sampled votes.
Data Analysis: DA = Descriptive Statistics + Inferential Statistics
Data analysis combines descriptive methods (like mean and median) and inferential methods (like hypothesis testing).
Response Rate: Response Rate = (Number of Responses / Total Sample Size) × 100
This metric helps evaluate the effectiveness of a data collection method.
Confidence Interval: CI = Mean ± Z(σ/√n)
This formula provides a range of values likely to contain the population mean based on sample data.
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