Question

Carrie is comparing the growth of plants under natural and artificial light sources.

Part A

Use the measures of center from the box plots to make an inference about the data.

Part B

Use the box plots to make an inference using the variability of the data.

Answer 1

A. Based on the median, the light source used in Group Q appears to more positively affect plant growth as compared to the light source used in Group P.

B. The data sets have the same IQR, so the natural and artificial light sources does not affect plant growth in both Group P and Group Q.

By critically observing the box plot shown above, we can logically deduce the following medians (best meausre of center) for both groups;

Median of group A = 2.

Median of group B = 3.5.

Part A.

Based on the medians, we can reasonably infer that the plants in Group P grew less on average, as compared to the plants in Group Q. Therefore, group Q has a greater growth of plants on average, under natural and artificial light sources because it has a greater median value of 3.5.

Part B.

Interquartile range (IQR) of group A = third quartile - first quartile

Interquartile range (IQR) of group A = 3 - 1.5

Interquartile range (IQR) of group A = 1.5

Interquartile range (IQR) of group B = 4.5 - 3

Interquartile range (IQR) of group B = 1.5

Based on the variability of the data, the range and IQR are the same in both group Q and group P, so they both have the same variability with respect to the growth of plants under natural and artificial light sources.

Answer 2

Median :

P = 2 ; Q = 3.5

Variability :

P = 1.5 ; Q = 1.5

Explanation:

The measure of center we can infer from the box plot is the median, which is the point marked by the vertical line in between the box ;

For Group P:

Median = 2 inches

For Group Q :

Median = 3.5 inches

To infer the variability :

We calculate the interquartile range (IQR) :

IQR = Q3 - Q1

Q3 = Upper quartile (end point of box) ; Q1 = lower quartile (start point of box) in the plot

Locate QI and Q3

Group P:

IQR = Q3 - Q1 = 3 - 1.5 = 1.5

Group Q :

IQR = Q3 - Q1 = 4.5 - 3 = 1.5