To draw the histogram for the given data using an initial class boundary of 1.5, an ending class boundary of 45.5, and 4 classes of equal width, we first need to determine the class width.
Class width = (Ending class boundary - Initial class boundary) / Number of classes
Class width = (45.5 - 1.5) / 4
Class width = 44 / 4
Class width = 11
Now, we can construct the histogram with the following steps:
1. Determine the class intervals:
Class 1: 1.5 - 12.5
Class 2: 12.5 - 23.5
Class 3: 23.5 - 34.5
Class 4: 34.5 - 45.5
2. Count the frequencies (number of occurrences) in each class interval:
Class 1 (1.5 - 12.5): 2
Class 2 (12.5 - 23.5): 2
Class 3 (23.5 - 34.5): 4
Class 4 (34.5 - 45.5): 6
3. Draw the histogram:
Each class interval will be represented by a rectangle, where the width of the rectangle corresponds to the class width and the height represents the frequency.
For the given data, the histogram will look like this:
Frequency
|
6 +----+
5 | |
4 + + +
3 | | | +
2 + + + +
1 | | | |
+----+----+----+----+
Class Intervals
1.5 12.5 23.5 34.5 45.5