Final answer:
The researcher should use a histogram to graph the counted instances of children's aggressive behaviors on the playground because it efficiently represents continuous quantitative data and shows the distribution of behavior frequencies.
Step-by-step explanation:
A researcher who observed and counted the number of times each child in his sample behaved aggressively while playing on a playground should use a histogram to graph his data. Histograms are used to represent the frequency distribution of a continuous variable, such as the measurement scale of aggression in this case. The x-axis of the histogram represents the range of aggression values, while the y-axis represents the frequency or count of children falling into each aggression range.
The type of graph that a researcher observed and counted the number of times each child behaved aggressively on a playground and would like to use to graph his data is a histogram. This choice is suitable because aggression is a large, continuous, quantitative dataset where the researcher has counted instances of a behavior, which are numerical in nature. The horizontal scale of a histogram represents classes of quantitative data values, and the heights of the bars correspond to frequency values. Since we are dealing with frequency data derived from observations which likely span various counts or ranges, a histogram provides a visual representation that clearly shows how the frequency of aggressive behaviors is distributed among children observed on the playground.