Question

A random selection of plants receiving two different types of treatments is measured for growth. The growth of the plants in each group is represented on the comparative box plot.

Two box-and-whisker plots. The first is titled, Treatment A, with left whisker 6, right whisker 11.25, left hand side of box 8, right hand side of box 9.5, and median 8.5. The second is titled, Treatment B, with left whisker 2, right whisker 7.5, left hand side of box 3.5, right hand side of box 6, and median 4.75.

What inference can be made from this sample data?



The range in growth for treatment B is much greater than the range in growth for treatment A.

Plants with treatment A in general grow more than plants with treatment B.

Both treatments have almost identical results in growth.

Plants with treatment B in general grow more than plants with treatment A.

Answer 1

Plant with treatment A in general grow more than plants with treatment B.

Picture below.

Answer 2

• Plants with treatment B in general grow more than plants with treatment A.

Explanation:

Treatment A:

Least value or minimum value= 6

Maximum value= 11.25

First quartile or lower quartile i.e.
`Q_1`= 8

Middle quartile or Median i.e.
`Q_2`= 8.5

Upper quartile or third quartile i.e.
`Q_3`= 9.5

Range= Maximum value-Minimum value

= 11.25-6

= 5.25

Interquartile range ( IQR)=
`Q_3-Q_1`

= 9.5-8

= 1.5

Treatment B:

Least value or minimum value= 2

Maximum value= 7.5

First quartile or or lower quartile i.e.
`Q_1` = 3.5

Middle quartile or Median i.e.
`Q_2`= 4.75

Upper quartile or third quartile i.e.
`Q_3`= 6

Range= Maximum value-Minimum value

= 7.5-2

= 5.5

Interquartile range ( IQR)=
`Q_3-Q_1`

= 6-3.5

= 2.5

The range in growth for treatment B is not much greater than the range in growth for treatment A.

( since there is a very less difference in range

5.5-5.25=0.25)

Since, the IQR as well range of treatment B is greater than treatment A.

Hence, Plants with treatment B in general grow more than plants with treatment A.