Final answer:
The range of a graph is found by identifying the lowest and highest points on the y-axis, and a histogram's bars represent the frequency of data within specified intervals. Constructing a histogram involves dividing the data into equal-width intervals and scaling the axes accordingly, aiding in the visual analysis of data distributions.
Step-by-step explanation:
To determine the range of a graph, you need to identify the lowest and highest values that the dependent variable (typically represented on the y-axis) takes on. For a given histogram, which is commonly used to represent frequency distributions, each bar height indicates the frequency or count of data within the interval it represents. Without a specific graph to reference, you'd generally look at the lowest and highest y-values present on the graph to determine the range. This might entail literally measuring the graph's lowest and highest points.
When constructing a histogram, you divide the data into intervals. Typically, you will choose five to six intervals, ensuring that each interval has the same width. For example, if the x-axis goes from 32.5 to 100.5 and there are five intervals, the width of each interval would be (100.5 - 32.5)/5 = 13.6. You then plot the frequency of data points within each of these intervals as bars on the histogram.
To further analyze data within a histogram, one might calculate probabilities or focus on specific intervals by shading areas of interest, which guides visual interpretation. This technique is often useful when trying to convey the proportion of data that lies between certain values.