Statistical Errors & Approximations – Types & Handling ⚠️📊
No data is perfect.
Even a well-planned statistical investigation contains errors, because statistics deals with large groups, human responses, and approximations.
Understanding errors is crucial because:
✔ It improves accuracy
✔ Helps identify weak points in data
✔ Ensures better decision-making
✔ Prevents misleading conclusions
What Are Statistical Errors?
Definition:
A statistical error is the difference between the true value and the observed/measured value.
Errors arise because we cannot measure everything perfectly.
Types of Statistical Errors 🧩
Statistical errors can be broadly classified into:
✔ 1. Sampling Errors
✔ 2. Non-Sampling Errors
✔ 3. Approximation Errors
✔ 4. Blunders/Human Errors
Let’s explore each with examples.
1. Sampling Errors 🎯
These occur when only a sample (part of the population) is studied instead of the whole population.
Causes:
- Small sample size
- Unrepresentative sample
- Wrong sampling method
Examples:
- Surveying only college students to estimate India's average income
- Taking 20 customers as sample for a supermarket study
Sampling errors decrease when sample size increases or when proper sampling methods are used.
2. Non-Sampling Errors 🚫
(These are more dangerous!)
These errors occur in both census and sample surveys.
Major Types:
a) Response Errors
Caused by respondents giving:
- Wrong answers
- Incomplete responses
- Over/understated values
Example: People lying about income or age.
b) Non-response Errors
Some respondents do not reply → reduces accuracy.
Example:
Online surveys usually get low response rates.
c) Enumerator Errors
Mistakes by investigators due to:
- Poor training
- Fatigue
- Careless recording
Example:
Interviewer mis-records “35,000” as “3,500”.
d) Processing Errors
Mistakes during:
- Editing
- Coding
- Data entry
- Tabulation
Example:
Typing error while entering survey data.
e) Instrument Errors
Faulty measuring tools.
Example:
Weighing machine showing ±2 kg variation.
3. Approximation Errors 🧮
Statistics deals with approximations because:
- Rounding is necessary
- Grouping into classes is used
- Averages may not represent individual values
Examples:
- Reporting population as “142 crore” instead of 142.3 crore
- Rounding off ₹12,49,587 to ₹12.50 lakh
- Mean income ≠ actual income of any individual
Why acceptable?
Approximations make data simple, usable, and comparable.
4. Blunders / Human Errors 🧍♂️💥
These are mistakes caused by:
- Carelessness
- Wrong units
- Incorrect calculations
- Typing errors
Example:
Reporting 120 instead of 12.
Blunders ≠ statistical errors.
They are avoidable mistakes caused by humans.
ASCII Diagram — Types of Statistical Errors
Sampling Errors
↓
Non-Sampling Errors (Response, Non-response, Enumerator, Processing, Instrument)
↓
Approximation Errors
↓
Blunders (Human mistakes)
How Can Errors Be Minimized? ✔️
1. Use Proper Sampling Methods
Random and stratified sampling reduce errors.
2. Increase Sample Size
Larger samples → more accuracy.
3. Train Investigators
Proper training reduces enumerator errors.
4. Use Pilot Surveys
Helps identify questionnaire issues.
5. Improve Instruments
Calibrated tools reduce measurement errors.
6. Careful Data Processing
Double-check coding, editing, and tabulation.
7. Avoid Over-Reliance on Averages
Use multiple measures (mean, median, mode).
Summary ✨
- Errors are unavoidable but can be minimized.
- Sampling errors arise from studying a part of the population.
- Non-sampling errors arise from response, enumerators, processing, and instruments.
- Approximation errors occur due to rounding and grouping.
- Blunders are avoidable human mistakes.
Quiz Time! 🎯
Test Your Knowledge
Question 1 of 5
1. Sampling error occurs when: