IntStorage.java

import java.io.*;

public class IntStorage {
    RandomAccessFile file;

    public IntStorage(String fileName) throws FileNotFoundException {
        this.file = new RandomAccessFile(fileName, "rw");
    }

    public void pushInt(int number) throws IOException {
        this.doPushInt(this.file, number);
    }

    public void readAll() throws IOException {
        this.doReadAll(this.file);
    }

    public void find(int number) throws IOException {
        this.file.seek(0);
        while (this.file.getFilePointer() < this.file.length()) {
            if (this.file.readInt() == number) {
                System.out.println(this.file.getFilePointer() / 4);
                return;
            }
        }
    }

    public void average() throws IOException {
        int count = 0;
        int sum = 0;

        this.file.seek(0);

        while (this.file.getFilePointer() < this.file.length()) {
            count += 1;
            sum += this.file.readInt();
        }

        System.out.println(sum / count);
    }

    public void sort() throws IOException {
        // Collect numbers in vector
        java.util.Vector<Integer> numbers = new java.util.Vector<Integer>();
        this.file.seek(0);
        while (this.file.getFilePointer() < this.file.length()) {
            numbers.addElement(this.file.readInt());
        }

        // Do the actual sorting.
        int size = numbers.size();

        for (int i = 0; i < size; i++) {
            int min = i;

            // Find smallest element in (numbers[i] ... numbers[size-1])
            // and swap it with numbers[i]
            for (int j = i+1; j < size; j++) {
                if (numbers.elementAt(j) < numbers.elementAt(min)) {
                    min = j;
                }
            }

            java.util.Collections.swap(numbers, i, min);
        }

        // numbers should be sorted by now
        for (int i = 0; i < size; i++) {
            System.out.println(numbers.elementAt(i));
        }
    }

    public void export(String evensFileName, String oddsFileName) throws IOException {
        RandomAccessFile evensFile = new RandomAccessFile(evensFileName, "rw");
        RandomAccessFile oddsFile = new RandomAccessFile(oddsFileName, "rw");

        // Overwrite files
        evensFile.setLength(0);
        oddsFile.setLength(0);

        this.file.seek(0);

        while (this.file.getFilePointer() < this.file.length()) {
            int number = this.file.readInt();

            if (number % 2 == 0) {
                this.doPushInt(evensFile, number);
            } else {
                this.doPushInt(oddsFile, number);
            }
        }

        System.out.println("Even numbers exported to " + evensFileName);
        this.doReadAll(evensFile);
        System.out.println("========");

        System.out.println("Odd numbers exported to " + oddsFileName);
        this.doReadAll(oddsFile);
        System.out.println("========");
    }

    public void doPushInt(RandomAccessFile file, int number) throws IOException {
        file.seek(file.length());
        file.writeInt(number);
    }

    public void doReadAll(RandomAccessFile file) throws IOException {
        file.seek(0);
        while (file.getFilePointer() < file.length()) {
            System.out.println(file.readInt());
        }
    }
}

Main.java

import java.io.*;

public class Main {
    static java.io.Console console = System.console();
    static IntStorage storage;

    static {
        try {
            storage = new IntStorage("./storage.dat");
        } catch (FileNotFoundException e) {
            throw new RuntimeException(e);
        }
    }

    public static void main(String[] args) throws FileNotFoundException {
        int option;

        try {
            while (true) {
                System.out.println("");
                System.out.println("Choose an option:");
                System.out.println("1 - Push a new integer into storage ");
                System.out.println("2 - Read all integers in storage ");
                System.out.println("3 - Find an integer and print it's position");
                System.out.println("4 - Print average for all integers in storage");
                System.out.println("5 - Print sorted list of integers");
                System.out.println("6 - Export storage filtered by even or odd");
                System.out.println("0 - Exit");
                System.out.println("");

                option = Integer.parseInt(console.readLine());

                System.out.println("");
                System.out.println("=========");
                System.out.println("");

                if (option == 0) {
                    return;
                } else if (option > 0 && option <= 6) {
                    switch (option) {
                        case 1: {
                            int number = Integer.parseInt(console.readLine("What number: "));
                            storage.pushInt(number);
                            break;
                        }
                        case 2: {
                            storage.readAll();
                            break;
                        }
                        case 3: {
                            int number = Integer.parseInt(console.readLine("What number: "));
                            storage.find(number);
                            break;
                        }
                        case 4: {
                            storage.average();
                            break;
                        }
                        case 5: {
                            storage.sort();
                            break;
                        }
                        case 6: {
                            storage.export("evens.dat", "odds.dat");
                            break;
                        }
                    }
                } else {
                    System.out.println("That's not a valid option");
                }
            }
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
}