Q.7 Which of the following is known as positional average?
(1) Mean deviation
(2) Standard deviation
(3) Median
(4) Mean
Positional Average Explained: MCQ Answer & Key Concepts
Positional averages (or positional measures of central tendency) are statistics determined by the position of values in an ordered dataset, not by their numerical magnitudes. In the MCQ: “Which of the following is known as positional average?” the correct answer is (3) Median.
The median is the middle value (50th percentile) in a ranked dataset, making it a true positional average. It’s robust against outliers, unlike arithmetic measures. Let’s examine all options systematically.
Correct Answer: Option (3) – Median
The median divides an ordered dataset into two equal halves—perfectly positional.
-
Calculation: For odd n, it’s the middle value; for even n, average of two middle values.
-
Example: Dataset {3, 7, 8, 12, 20} → Median = 8 (3rd position).
-
Why Positional? Depends only on order/rank, not actual values. Change 20 to 2000? Median stays 8.
Textbooks like Fundamentals of Mathematical Statistics (Gupta & Kapoor) explicitly classify median as positional average.
Why Not the Other Options? Complete Analysis
-
Option (1) Mean Deviation: Measure of dispersion, not central tendency. Calculated as ∑∣xi−xˉ∣n. Uses all values’ distances from mean—no positional nature.
-
Option (2) Standard Deviation: Dispersion measure: σ=∑(xi−xˉ)2n. Arithmetic calculation, sensitive to extreme values. Not positional or central tendency.
-
Option (4) Mean: Arithmetic average: xˉ=∑xin. Uses magnitude/sum of all values, not positions. Outliers heavily influence it (e.g., {1,2,3,100} mean=26.5 vs. median=2.5).
Comparison Table: Positional vs. Arithmetic Measures
| Option | Type | Calculation Method | Affected by Position? | Affected by Magnitude? |
|---|---|---|---|---|
| (1) Mean Deviation | Dispersion | Distance from mean | No | Yes |
| (2) Standard Dev. | Dispersion | Squared distance | No | Yes |
| (3) Median | Positional Avg | Middle position | Yes | No |
| (4) Mean | Arithmetic Avg | Sum ÷ count | No | Yes |
Applications in Biology, Research & Exams
Median shines in skewed biological data (gene expression, microbial counts) where outliers (experimental errors) skew means. Essential for CSIR NET, GATE Statistics, and biostats—distinguishing positional (median, mode, quartiles) from arithmetic (mean) measures tests core concepts.
Pro Tip: Positional averages = {Median, Mode, Percentiles/Quartiles}. Arithmetic = {Mean}.
