Final answer:
A back-to-back stem-and-leaf plot is constructed to compare the growth of two plant varieties by separating data into stems and leaves, with the goal of evaluating the effects of plant food on growth.
Step-by-step explanation:
The question involves constructing a back-to-back stem-and-leaf plot to compare the growth of two varieties of plants. This type of plot is useful in displaying the data sets in a visually organized manner, allowing for easy comparison of the distributions.
To create the stem-and-leaf plot, separate each data value into a stem and a leaf. The stem is composed of the leading digits and the leaf is the last significant digit. For instance, if the growth is '23 cm', then '2' is the stem and '3' is the leaf. You start by listing stems in a vertical line, and then place leaves on each side of the stems, one side for each variety of plant. The leaves should be arranged in ascending order for clarity.
Comparing the distributions can shed light on whether the food given to the plants, a variable that the researcher believes affects growth, is making the plants grow taller. By examining the shape and spread of the data on the plot, one can infer differences in plant growth between the two groups.