Which of the following statement is incorrect about histograms?

The rectangles in a histogram are all adjacent and there is some open space between two consecutive rectangles.

The correct answer is Option 1: The rectangles in a histogram are all adjacent and there is some open space between two consecutive rectangles. 

Option 1: The rectangles in a histogram are all adjacent and there is some open space between two consecutive rectangles. This statement is incorrect because in a histogram, the rectangles (or bars) are adjacent to each other without any open space between them. The absence of gaps indicates that the data is continuous and covers the entire range without interruption.

Option 2: The width in a histogram is as important as its height. This statement is correct. In a histogram, the width of each bar represents the interval of the data, while the height represents the frequency (or count) of data points within that interval. Both width and height are crucial for accurately representing the distribution of the data.

Option 3: A histogram is a two-dimensional diagram. This statement is correct. A histogram is indeed a two-dimensional diagram where the x-axis represents the data intervals (or bins) and the y-axis represents the frequency of data points in those intervals.

Option 4: It is a set of rectangles with base as the intervals between class boundaries (along X-axis) and with areas proportional to the class frequency. This statement is correct. The base of each rectangle in a histogram corresponds to the interval between class boundaries on the x-axis, and the area (or height, if the width is constant) of each rectangle is proportional to the frequency of data points within that interval. This helps visualize the distribution of data across different intervals.