(6.4) Measuring the Spread of Data - Continuous Data
We learned in measuring the center of continuous data that we could estimate the median from a cumulative frequency curve.
| Weight ($x$ kg) in class intervals |
Frequency | Cumulative Frequency |
|---|---|---|
| $\phantom{30 \le}\; x \lt \color{red}{40}$ | $0$ | $\color{red}{0}$ |
| $40 \le x \lt \color{red}{50}$ | $10$ | $\color{red}{10}$ |
| $50 \le x \lt \color{red}{60}$ | $18$ | $\color{red}{28}$ |
| $60 \le x \lt \color{red}{70}$ | $13$ | $\color{red}{41}$ |
| $70 \le x \lt \color{red}{80}$ | $15$ | $\color{red}{56}$ |
| $80 \le x \lt \color{red}{90}$ | $4$ | $\color{red}{60}$ |
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 th person's weight and the upper quartile ($Q_3$) is the th person's weight.
$Q_1=$
kg
$Q_3=$
kg
Interquartile Range $=$
kg
Estimate the number of people who weigh less than or equal to 56 kg.
people
Estimate the number of people who weigh more than or equal to 76 kg.
people
Percentiles
Find:
$50\%$ of $60=$
$60\%$ of $60=$
$90\%$ of $60=$
The 50th percentile is the weight which 50% of the people are less than. The 50th percentile =
kg
The 60th percentile is the weight which 60% of the people are less than. The 60th percentile =
kg
The 90th percentile is the weight which 90% of the people are less than. The 90th percentile =
kg
Standard Deviation
To estimate the standard deviation for continuous data, we use the mid-interval values as we did when estimating the mean.| Weight ($x$ kg) in class intervals |
Mid-interval Value |
Frequency |
|---|---|---|
| $40 \le x \lt 50$ | $45$ | $10$ |
| $50 \le x \lt 60$ | $55$ | $18$ |
| $60 \le x \lt 70$ | $65$ | $13$ |
| $70 \le x \lt 80$ | $75$ | $15$ |
| $80 \le x \lt 90$ | $85$ | $4$ |