Question

what is the class boundary between the first and second classes?
class boundary = 3
question 18
1 pt 1 details
data was collected for 40 randomly selected trees growing in the median strip of a busy freeway. the height of each tree (in inches) was recorded. data was recorded to the nearest whole inch. the data is summarized in the histogram below.
what is the minimum possible tree height for the data recorded for this histogram? note: each class contains its lower class boundary, but not its upper class boundary.
minimum = enter an integer or decimal number more..

Explanation:

Step1: Understand class boundaries

Class boundaries are calculated as the mid - point between the upper limit of one class and the lower limit of the next class. For the first class \(25 - 30\) and the second class \(30 - 35\) (assuming the first histogram class is \(25 - 30\) based on the x - axis of the histogram).

The formula for the class boundary between two consecutive classes with lower class limit \(L_2\) (of the second class) and upper class limit \(U_1\) (of the first class) is \(b=\frac{U_1 + L_2}{2}\). Here, \(U_1 = 30\) and \(L_2=30\). But wait, since the data is recorded to the nearest whole inch, if we consider the first non - zero class (assuming the first bar on the histogram starts at \(25\)). The first class is \(24.5 - 29.5\) (because when data is rounded to the nearest whole number, the class boundaries for a class like \(25 - 30\) (recorded values) are \(24.5 - 29.5\)). The second class (recorded as \(30 - 35\)) has boundaries \(29.5 - 34.5\).

Step2: Calculate the class boundary

Using the formula \(b=\frac{29.5+29.5}{2}\) (the upper boundary of the first non - zero class \(24.5 - 29.5\) is \(29.5\) and the lower boundary of the next class \(29.5 - 34.5\) is \(29.5\)). But if we consider the first class shown in the histogram (x - axis starts at \(25\)), for a class like \(25 - 30\) (recorded data), the actual class boundaries (to account for rounding) are \(24.5 - 29.5\). The next class (recorded as \(30 - 35\)) has boundaries \(29.5 - 34.5\). The class boundary between them is \(29.5\).

For the minimum height:

Step1: Consider the class boundaries

Since each class contains its lower class boundary but not its upper class boundary. The first class (assuming the first bar on the histogram) has a lower class boundary. If the first class (in terms of recorded data \(25 - 30\)) has actual boundaries \(24.5 - 29.5\) (because when data is rounded to the nearest whole number, if \(x\) is the actual height and \(y\) is the recorded height (\(y=\lfloor x + 0.5
floor\)), then for \(y = 25\), \(x\geq24.5\))

Answer:

The class boundary is \(29.5\) and the minimum possible tree height is \(24.5\)