Quartiles

Topic Content:

The quartile divides the distribution into four equal parts. When n is large they are given as Lower quartile Q₁ = \( \frac{n}{4} \scriptsize th \; value \)

Middle Quartile or Median Q₂ = \( \frac{n}{2} \scriptsize th \; value \)

Upper Quartile Q₃ = \( \frac{3n}{4} \scriptsize th \; value \)

However, when n ≤ 50 (i.e. discrete)

Q₁ = \( \frac{n+1}{4} \scriptsize th \; value \)

Q₂ = \( \frac{n+1}{2} \scriptsize th \; value \)

Q₃ = \( \frac{3(n+1)}{4} \scriptsize th \; value \)

Interquartile Range:

The interquartile range is the difference between the upper quartile and the lower quartile. i.e.

Interquartile range = \( \scriptsize Q_3 \: -\: Q_1 \)

Semi-interquartile Range:

Semi-interquartile range can be found by:

\( \scriptsize Q = \normalsize \frac{1}{2} \scriptsize\left(Q_3 \: -\:Q_1 \right) \)

Percentiles:

Definition: The percentile divides the data into 100 equal parts, a vertical axis is drawn on the right-hand side of the cumulative frequency curve/Ogive and marked 0% to 100%.

• The lower quartile or 1^st quartile is the 25^th percentile
• The median or the 2^nd quartile is the 50^th percentile
• The upper quartile or 3^rd quartile is the 75^th percentile

Example 5.2.1: