📦➖ Box-and-Whisker Brilliance: Mastering Data Spread!

Box-and-whisker plots are a compact way to display how data are spread out. **Being able to construct and interpret them quickly helps you spot medians, ranges, and outliers at a glance—skills that exam questions love to test!**

The Core Idea

A box-and-whisker plot summarises five key values: **minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum**. The "box" spans from

Q_1

Q_3

and encloses the middle 50\% of the data, while the "whiskers" reach out to the minimum and maximum.

Key point 1: Find the median by locating the middle value or averaging the two middle values when $n$ is even.
Key point 2: Quartiles divide the data into four equal parts— $Q_1$ is the median of the lower half, $Q_3$ of the upper half.

Worked Example: Exam Scores Snapshot

Problem: The mathematics scores of 11 students are: 42, 55, 61, 65, 68, 70, 72, 75, 78, 82, 90. Construct a box-and-whisker plot and interpret the distribution.

Step 1: Sort the data (already sorted) and locate the median
$Q_2 = 70$
.
Step 2: Determine $Q_1$ (median of lower half):
$Q_1 = 61$
and $Q_3$ (median of upper half):
$Q_3 = 78$
.
Step 3: Identify minimum
$\min = 42$
and maximum
$\max = 90$
, then draw whiskers to these points.
Step 4: Interpret: The middle 50\% (from $61$ to $78$ ) is fairly tight, indicating consistent majority performance, while a long lower whisker shows a few low scores pulling the range downward.

Practice drawing several plots back-to-back for comparison—**the more you sketch, the faster you’ll recognise trends on exam day!** Keep sharpening those graphing pencils and watch your data-handling marks soar.