Tally Lab - YOU ONLY NEED PARTS 1 and 2

Background
A researcher wishes to calculate some statistical properties for a collection of
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

Assignment Part 1 - "Tally" array

• Write a program to recreate the above researcher's frequency list.
• Here's a trick to use:
  • If the random values range from 0..15, create a count array
    (count[0], count[1], ..., count[15])
  • Initialize the counts to 0
  • count[value]++ (or count[value] = count[value] + 1) to increment the counts

• Using the "tally" array from part 1, write a function to find the maximum frequency.
  In tally above, findMax(tally) returns 10
• Syntax for this C function:
  int findMax(int tally[]) {
  . . .
  return maxFreq;
  }

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• Using the "tally" array from part 1, write a calculateModes() that
  returns an int array containing the mode(s) found in tally.
• The length of this mode array is equal to the number of modes.
• A mode is a value that occurs with maximal frequency. If there is more
  than one such value, each is considered a mode of the data.
• In tally above, the modes are 2, 4, and 11 because they occur 10 times
  and all other values occur fewer than 10 times.
  (mode[0]=2, mode[1]=4, mode[2]=11)
• In writing calculateModes() you should call the function findMax() written in 1.6
• Syntax for this C function (I think arrays are returned only as parameters):
  void calculateModes(int tally[], int modes, ...) {
  . . .
  // modes array calculated here
  }

• Write the function kthDataValue() that returns the kth data value
  when the data values are considered in sorted order. The indexes of the tally array
  represent possible data values and each array location contains the frequency of the value corresponding to its index.
• In the tally array above, 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, 1) returns 2, kthDataValue(tally, 14) returns 3,
  kthDataValue(tally, 15) returns 3, and kthDataValue(tally, 16) returns 4