Final answer:
The class boundary for the 13-14 class in a histogram where y is measured to the nearest whole number is from 12.5 to 14.5. Histogram bars represent class intervals and should be calculated for consistent representation without values falling on boundaries.
Step-by-step explanation:
The class boundary for the 13-14 class when variable y is measured to the nearest whole number is typically taken to be the numbers that lie exactly halfway between the ending of one class and the beginning of the next. In this case, the class boundary would be from 12.5 to 14.5. This is because the class labeled 13-14 actually represents all the values from just above 12 to just below 15, due to the measurement being taken to the nearest whole number. Hence, the boundaries are calculated by adding 0.5 to the upper limit and subtracting 0.5 from the lower limit.
Constructing a histogram includes calculating the width of the bars or class intervals. The width of each bar represents the range of data within that class. The width is determined by calculating the difference between the upper and lower class boundaries. If you are asked to draw a histogram bar with a specific physical width and height, the physical width represents the class width, and the height represents the frequency or relative frequency of the class.
To ensure no data value falls on a boundary, it is a common practice to slightly adjust the endpoints by a small amount, often following a rounding rule. For example, if a height is 60 inches, rounding the boundary down to 59.95 prevents the value from falling exactly on the boundary.
Considering consistency and clarity during histogram construction is crucial, as having too many or too few bars can affect the visualization's effectiveness in representing the distribution of data values.