Final answer:
Drawing a smooth curve through the tops of the bars in a histogram helps to visualize the overall distribution of the data. The curve should be described in relation to its shape, peaks, and symmetry to give insight into the data's characteristics like skewness or modality.
Step-by-step explanation:
When constructing a histogram, drawing a smooth curve through the tops of the bars represents the overall distribution of the data. This can help identify patterns, such as if the data has a single peak or multiple peaks, or if there is any skewness to the data. When you are asked to draw such a curve and describe its shape, it is important to look for specific characteristics like symmetry, skewness, or modality.
To describe the general shape of the curve, pay attention to whether the graph has a uniform distribution, where it might go straight across, or if it has a distinctive shape like a V or a hump. The curve might also be described as having a sharp process or a small, rounded process if it rises or falls sharply at any point. If the data has a peak or trough, the smooth curve will illustrate this by having a corresponding hump at that position within the histogram.
The general shape of the smooth curve can be described as, for example, "The smooth curve shows a unimodal distribution with a peak towards the left, indicating a skew to the right." or "The curve forms a bell shape, suggesting the data is normally distributed.". These descriptions provide a simple yet informative overview of the data's graphical representation.