APCS Free Response 2002 A1 Java Version

A1

A researcher wishes to calculate some statistical properties for a collection of integer data values. The data values are represented by the array tally. The indexes of the array represent the possible values of the actual data values from zero to the maximal value (15 in the example below). Each array location contains the frequency (number of occurrences) of the value corresponding to its index. In the example below, tally[4] is 10, which means that the value 4 occurs ten times in the collection of data; whereas tally[8] is 0, which means that the value 8 does not occur in the data collection.

    tally

Value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Frequency 0 0 10 5 10 0 7 1 0 6 0 10 3 0 0 1

Part A

You will write the static method calculateModes of the class Stats which is described as follows. Method calculateModes returns an int array which contain the mode(s) found in parameter tally The length of the returned array is equal to the number of modes A mode is defined as a value that occurs with maximal frequency. If there is more than one such value, each is considered a mode of the data. In the example above, the modes are 2, 4, and 11, because they each occur 10 times and all other values occur fewer than 10 times.

In writing calculateModes you may call the Stats method findMax specified below which returns the maximum value in array. Using the example array, findMax(tally) returns 10. Do NOT write findMax.

  /**
   * precondition: nums.length > 0
   * postcondition: returns the maximal value in nums
   */

  private static int findMax(int[] nums)

            Do NOT write the body of findMax

In writing calculateModes, you may call method findMax specified above.

Complete method calculateModes below.

  /**
   * precondition: tally.length > 0
   * postcondition: returns an int array that contains the modes(s);
   *                the array's length equals the number of modes.
   */

  public static int[] calculateModes(int[] tally)

Part B

You will write the method kthDataValue of the Stats class which is described as follows. Method kthDataValue returns the kth data value when the data values are considered in sorted order. Recall that the indexes of the array represent possible data values and that each array location contains the frequency of the value corresponding to its index.

In the example reprinted below, the first ten data values are 2, the next five data values are 3, and the next ten data values are 4. For this example, kthDataValue(tally, 1) returns 2, kthDataValue(tally, 14) returns 3, kthDataValue(tally, 15) returns 3, and kthDataValue(tally, 16) returns 4.

Value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Frequency 0 0 10 5 10 0 7 1 0 6 0 10 3 0 0 1

Complete method kthDataValue below.

  /**
   * precondition: tally.length > 0;
   *               0 < k <= total number of values in data collection
   * postcondition: returns the kth value in the data collection
   *                represented by tally
   */

  public static int kthDataValue(int[] tally, int k)

Owen L. Astrachan

Last modified: Wed Jul 10 12:05:23 EDT 2002