📊 Measure of Position (Statistics)

Last Updated: Jan 2026

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Measure of Position tells us where a data value lies relative to the rest of the data.

• Helps in ranking, comparison, and distribution analysis

🗣 Hinglish Tip: Measure of position = data me tum kis jagah khade ho (top, middle, bottom)

There are three main measures of position:

1. Percentiles
2. Quartiles
3. Interquartile Range (IQR)

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Percentiles

The k-th percentile (Pk) is the value below which k% of observations lie.

• It is divided data into 100 equal parts.An each part is percentile represent position of data.
• 50th percentile = Median
• 90th percentile = Top 10% cutoff

Formula (Ungrouped Data)

Position = (k / 100)(n + 1)

IF Position in fraction,

Result = lowerPosition + fractionValue*(upperPosition - lowerPosition) like Position = 2.25, lowerPosition = 2, upperPosition = 3, fractionValue = 0.25

Where:

• k = percentile number
• n = total observations

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Example

Data: 5, 7, 10, 12, 15, 18, 20, 25 Find P25

Step	Calculation	Result
n	Total values	8
Position	(25/100) × (8+1)	2.25
Value	Between 2nd & 3rd	≈ 7.75

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Quartiles

Quartiles divide data into 4 equal parts.

Quartile	Meaning
Q1	25% data below
Q2	50% (Median)
Q3	75% data below

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Formula (Ungrouped)

Qₖ = k(n + 1) / 4

Where k = 1, 2, 3

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Example

Data: 5, 7, 10, 12, 15, 18, 20, 25

Quartile	Position	Value
Q1	(1×9)/4 = 2.25	≈ 7.75
Q2	(2×9)/4 = 4.5	≈ 13.5
Q3	(3×9)/4 = 6.75	≈ 19.5

🗣 Hinglish Tip: Q1 = lower data, Q2 = beech ka data, Q3 = upper data

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Interquartile Range (IQR)

IQR measures the spread of middle 50% data.

IQR = Q3 − Q1

• Use for outlier detection
  • Lower bound = Q1 - 1.5IQR
  • Upper bound = Q3 + 1.5IQR
  • Outlier = Value > Upper bound or Value < Lower bound

Example

From above:

• Q3 = 19.5
• Q1 = 7.75

IQR = 19.5 − 7.75 = 11.75

🗣 Hinglish Tip: Interquartile Range = middle 50% data ka failaav

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