Question

1. maximum mark: 6

palvinder breeds labrador puppies at his farm. over many years he recorded the weight (g) of the puppies. the data is illustrated in the following box and whisker diagram.
(a) write down the median weight of the puppies. 1
(b) write down the upper quartile. 1
(c) find the interquartile range. 2
(d) find the weight of the heaviest possible puppy that is not an outlier. 2

Explanation:

Part (a)

Step1: Recall median in box - whisker plot

In a box - whisker diagram, the median is represented by the line inside the box. From the given box - whisker plot, we can see that the line inside the box is at 200 g.

Step1: Recall upper quartile in box - whisker plot

The upper quartile ($Q_3$) is the right - hand end of the box in a box - whisker diagram. From the plot, the right - hand end of the box is at 240 g.

Step1: Recall interquartile range formula

The interquartile range (IQR) is calculated as $IQR = Q_3-Q_1$, where $Q_1$ is the lower quartile and $Q_3$ is the upper quartile.

Step2: Find $Q_1$ and $Q_3$

From the box - whisker plot, the lower quartile ($Q_1$) is 190 g (left - hand end of the box) and the upper quartile ($Q_3$) is 240 g (right - hand end of the box).

Step3: Calculate IQR

$IQR=Q_3 - Q_1=240 - 190 = 50$

Answer:

200 g

Part (b)