Final answer:
To find the midpoint of the class with the highest frequency in a histogram, one should observe the bar with the tallest height and average its lower and upper boundaries. The midpoint is not estimated by other means such as calculating the mean of all ages or counting total classes.
Step-by-step explanation:
To determine the midpoint of the class with the highest frequency in a histogram, one should observe the histogram bar with the greatest height. This represents the class interval with the highest frequency. The midpoint can then be found by identifying the lower and upper class boundaries of this interval and calculating the average of these two numbers. This is done by adding the lower boundary to the upper boundary and then dividing by two. The midpoint is not found by counting the total number of ages, calculating the mean of all ages, nor by counting the total number of classes in the histogram.
For example, if the tallest bar in the histogram covers the age range of 20-29 years, the midpoint of this class would be (20+29)/2, which is 24.5 years. The midpoint provides a useful measure of central tendency for that particular class interval.
Important points in constructing a histogram:
- Determine the number of bars or classes and maintain consistency. For clarity, 5-15 bars or classes are common.
- Decide the width of each bar by dividing the range of the data by the number of bins (consistent bin size).
- Find the midpoint for each class to plot on the x-axis, corresponding with the frequency on the y-axis.
- For displaying qualitative data like car colors, a bar graph is more suitable.