Box Plots GCSE Questions, Worked Examples and Answers

The line inside the box shows the $\boxed{\text{median}}$.

Read the box edges: $Q_1=20$ and $Q_3=52$.

$\text{IQR}=52-20=\boxed{32}$

Read the two whisker ends.

$\text{Range}=68-11=\boxed{57}$

Use one linear scale. Draw the box from $18$ to $45$, place the median at $32$, and extend the whiskers to $6$ and $72$.

The 6th value is the median.

$\text{median}=14$

The lower and upper halves each contain five values.

$Q_1=7,\qquad Q_3=23$

$\boxed{\text{five-number summary: }3,7,14,23,31}$

Group A has the higher median because $38>34$, so its typical value is higher.

$\text{IQR}_A=48-24=24$

$\text{IQR}_B=58-18=40$

Group A has the smaller IQR, so it is more consistent.

$\boxed{\text{A has a higher typical value and less spread than B.}}$

It represents an unusually high observation that has been classified as an outlier under the rule used for this plot.

$\boxed{\text{a high outlier}}$

$\text{IQR}_A=57-51=6\text{ g}$

$\text{IQR}_B=60-48=12\text{ g}$

$\boxed{\text{Machine A is more consistent because its IQR is smaller.}}$

Team Blue has the higher median, so it typically scored more.

Team Red has the smaller IQR, so its middle half of scores is less spread out.

$\boxed{\text{Blue typically scored higher, but Red was more consistent.}}$

About $75\%$ of values are at or above the lower quartile.

$0.75\times160=120$

$\boxed{\text{About }120\text{ deliveries}}$

Use the same value scale. Draw the box from $21$ to $49$, the median at $33$, and whiskers to $5$ and $75$.

$Q_1=Q_3-\text{IQR}$

$Q_1=46-19=\boxed{27}$

Quartiles divide ordered data into four equal groups. The lengths show spread, not how many observations lie in each group.

$\boxed{\text{about }25\%\text{ in each section}}$

P has the larger overall range, so its full set is more spread out.

Q has the larger IQR, so its middle half is more spread out.

$\boxed{\text{The two spread measures lead to different comparisons.}}$

There are $15$ values. The quartile positions are

$Q_1:\ \frac{15+1}{4}=4\text{th value}$

$\text{median}:\ \frac{15+1}{2}=8\text{th value}$

$Q_3:\ \frac{3(15+1)}{4}=12\text{th value}$

So $Q_1=9$, the median is $18$ and $Q_3=34$.

$\boxed{2,\ 9,\ 18,\ 34,\ 44}$