Measures of Position Vocabulary (Quartiles, Deciles, Percentiles)

Vocabulary flashcards covering quartiles, deciles, percentiles, percentile ranks, and associated methods (Mendenhall & Sincich, interpolation) as used in the measures-of-position module.

Quartiles

Values that divide a data set into four equal parts: Q1 (lower quartile), Q2 (median), and Q3 (upper quartile).

Q1 (Lower Quartile)

The value below which 25% of data fall; position commonly ¼(n+1) for ungrouped data in ascending order.

Q2 (Median)

The middle value that divides the data into two halves; position ½(n+1); also known as the 50th percentile (P50).

Q3 (Upper Quartile)

The value below which 75% of data fall; position ¾(n+1).

Interquartile Range (IQR)

Spread of the middle 50% of data: IQR = Q3 − Q1.

Quartile Deviation (QD)

Half of the interquartile range: QD = (Q3 − Q1)/2.

Position (order statistics)

The index used to locate a quartile within the ordered data; fractional positions may require interpolation.

Mendenhall and Sincich Method

A method for finding quartiles/deciles using fractions of (n+1) with specific rounding rules (e.g., round up for L, round down for U).

Dk (Decile)

Nine points that divide a data set into ten equal parts: D1, D2, …, D9; position Dk = k/10 (n+1) (M&S or similar rule).

D1 (First Decile)

The 10th percentile; position D1 = 1/10 (n+1).

D9 (Ninth Decile)

The 90th percentile; position D9 = 9/10 (n+1).

Percentiles

Quantiles that divide a data set into 100 equal parts; Pk denotes the kth percentile; position Pk = k/100 (n+1).

P50 (50th Percentile)

The same as the median; the value below which 50% of data fall.

Percentile Rank

The percentage of values below or equal to a given value; for ungrouped data: (numbers below x + 0.5) / n × 100%.

Pk (Percentile)

The value at the kth percentile in the ordered data (e.g., P16, P77).

Ungrouped Data

A data set listed individually, not in classes or groups.

Interpolation (percentiles/quartiles)

Estimating a percentile/quartile when the required position falls between data points by linear interpolation.

Pk Position

The index where Pk lies: Position of Pk = k/100 × (n+1).

Data Arranged in Ascending Order

Sorting data from smallest to largest before computing order statistics.

P50 Equals Median

P50 is the same value as the median.

Lower vs Upper Quartile Interpretations

Q1 marks the 25th percentile; Q3 marks the 75th percentile.

Percentile vs Percentile Rank (Distinction)

Percentile is a value; percentile rank is the percentage of scores below that value.

Ten-Part Division Concept

Dividing data into ten parts using deciles, with D1–D9 as cut points.

Position Formulas (General Idea)

For quartiles/deciles/percentiles, use fractions of (n+1) to locate the position; interpolation may be used when non-integer.

Order Statistics in Ungrouped Data

Calculations rely on the sorted list and the (n+1) position rules.

Quartile Deviation vs IQR

QD is half of IQR; IQR measures spread of middle 50%.

Percentile Rank Interpretation

Indicates the percentage of the norm group scoring at or below a given value.

Example Relationship

Q2 = P50; D5 often corresponds to the median in the decile framework; P75 = Q3.