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(6.4) Measuring the Spread of Data - Continuous Data

Weight ($x$ kg)
in class intervals
Frequency Cumulative
Frequency
$\phantom{30 \le}\; x \lt \color{red}{40}$ $0$ $\color{red}{0}$
$40 \le x \lt \color{red}{50}$ $10$ $\color{red}{10}$
$50 \le x \lt \color{red}{60}$ $18$ $\color{red}{28}$
$60 \le x \lt \color{red}{70}$ $13$ $\color{red}{41}$
$70 \le x \lt \color{red}{80}$ $15$ $\color{red}{56}$
$80 \le x \lt \color{red}{90}$ $4$ $\color{red}{60}$
alt-text

Interquartile Range
Using this curve, we can also estimate the lower quartile ($Q_1$), upper quartile ($Q_3$) and hence the interquartile range.

If the median is the $30$th person's weight, the lower quartile ($Q_1$) is the