Final answer:
The incorrect statement regarding frequency distributions is that the width of the class intervals can be different (option 4). Typically, class intervals should be of equal width for consistent data representation in histograms.
Step-by-step explanation:
With respect to frequency distributions, the statement that is not true is that "The width of each of the class intervals can be different." For an accurate representation in histograms and frequency tables, class intervals should generally be of equal width to ensure that each bar or interval represents the same range of data.
However, there might be exceptions in certain cases, especially when working with grouped data or displaying relative frequencies.
Frequency distributions are indeed used as a more efficient way of arranging data. While it's generally recommended to have between 10 and 20 class intervals, this is not a strict rule and can be adjusted according to the specifics of the data set. The class intervals should be continuous and mutually exclusive to ensure that each data value falls into one and only one interval.
In particular, there could be different conventions for which endpoint is included in the interval, but within a single frequency distribution, this practice should be consistent. Typically, the left boundary is included, and the right is not, except for the first interval, which may include both.
Histograms are graphical versions of frequency distributions, and they show contiguous rectangles with the height of each rectangle representing the frequency of the respective data class. The histogram's bars are of equal width, and the midpoints of class intervals are named on the x-axis. This accuracy in presentation is crucial to correctly interpret the graphical representation of the data.