Final answer:
The subject is constructing a Huffman tree for given integers and their occurrences, determining the Huffman codes, and also creating a histogram using intervals and graphing appropriately.
Step-by-step explanation:
Constructing the Huffman Tree
To construct the Huffman tree for the given integers, first list them with their occurrences:
- 82 - 416
- 664 - 97
- 327 - 212
- 349 - 509
- 423 - 446
- 389 - 74
Next, start by combining the two integers with the lowest occurrences, which are 389 and 664. Continue combining the trees with the lowest total occurrences, creating a binary tree where each parent node is the sum of its child nodes' occurrences, until there is only one tree remaining, which represents the Huffman tree. The Huffman code for each integer is determined by the path from the root of the tree to the integer; a left turn corresponds to a '0' and a right turn corresponds to a '1'.
Huffman Codes
The Huffman codes for the integers can be found by reading the paths from the root of the Huffman tree to each corresponding leaf (integer). For instance, if the path to the integer '82' is left, left, right; its Huffman code would be '001'.
Constructing a Histogram
To create a histogram based on a set of data values, divide the range of your data into equal intervals and count how many data points fall into each interval. Then, draw a bar for each interval on a graph with the height of the bar representing the number of data points in that interval. Make sure to use a ruler and pencil for accuracy and scale the axes properly.