Final answer:
Histograms can display both frequency and relative frequency, with the former being a count of data occurrence and the latter indicating the proportion of the dataset that falls within each category. They are used to visually analyze the distribution of large, continuous, quantitative data sets and can provide insights into the data's shape, center, and spread.
Step-by-step explanation:
Histograms can display both the frequency and relative frequency of measurements. Frequency refers to the count of how many times a particular data point or category appears within a dataset. In contrast, relative frequency indicates the proportion of data points that fall within each category or data range, often represented as a percentage. This differentiation is significant when analyzing data distributions, as absolute numbers don't always provide a complete understanding without considering the context of the overall dataset size.
A histogram consists of contiguous (adjoining) boxes, with the horizontal axis representing the variable's categories or intervals, and the vertical axis labeled either with frequency or relative frequency. The overall shape of the histogram can give insights into the distribution's form, such as whether it's normal, approximately normal, or skewed in some direction. It is generally used with large, continuous, quantitative data sets to visually present and analyze the data thoroughly.
For example, if you have a class of 35 students and seven students received scores in the 70–79 range, the relative frequency of scores in this range would be the proportion of students from the whole class, which can be calculated by dividing the number of students in that score range by the total number of students. When constructing a histogram, it is essential to determine the scale and intervals properly, considering the variations in data set ranges and how they are grouped.