Measure of Position (Statistics)

Last Updated: Jan 2026

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

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

There are three main measures of position:

Percentiles

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

It divides data into 100 equal parts. Each part represents a percentile position in the data.
50th percentile = Median
90th percentile = Top 10% cutoff

Formula (Ungrouped Data)

 $\text{Position} = \left(\frac{k}{100}\right)(n + 1)$

If Position is a fraction:

 $\text{Result} = \text{lowerPosition} + \text{fractionValue} \times (\text{upperPosition} - \text{lowerPosition})$

Like:

 $\text{Position} = 2.25$

 $\text{lowerPosition} = 2$

 $\text{upperPosition} = 3$

 $\text{fractionValue} = 0.25$

Where:

Example

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

Find $P_{25}$

Quartiles divide data into 4 equal parts.

Formula (Ungrouped)

 $Q_k = \frac{k(n + 1)}{4}$

Where $k = 1, 2, 3$

Example

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

🗣 Hinglish Tip: $Q_1$ = lower data, $Q_2$ = beech ka data, $Q_3$ = upper data

IQR measures the spread of middle 50% data.

 $IQR = Q_3 - Q_1$

Use for outlier detection
- Lower bound = $Q_1 - 1.5IQR$
- Upper bound = $Q_3 + 1.5IQR$
- Outlier = Value > Upper bound or Value < Lower bound

Example

From above:

 $IQR = 19.5 - 7.75 = 11.75$

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