11.5. Checking the other values

how_many only counts the occurrences of a particular value, and we are interested in seeing how many times each value appears. We can solve that problem with a loop:

int num_values = 20;
int upper_bound = 9;
std::vector<int> numbers = make_vector (num_values, upper_bound);

std::cout << "value\thow_many";

for (int i = 0; i<=upper_bound; ++i) {
  std::cout << i << '\t' << how_many (numbers, i) << '\n';
}

Notice that it is legal to declare a variable inside a for statement. This syntax is sometimes convenient, but you should be aware that a variable declared inside a loop only exists inside the loop. If you try to refer to i later, you will get a compiler error.

This code uses the loop variable as an argument to how_many, in order to check each value between 0 and 9, in order. The result is:

value   how_many
0       2
1       1
2       3
3       3
4       0
5       2
6       5
7       2
8       0
9       2

Again, it is hard to tell if the digits are really appearing equally often. If we increase num_values to 100,000 we get the following:

value   how_many
0       10130
1       10072
2       9990
3       9842
4       10174
5       9930
6       10059
7       9954
8       9891
9       9958

In each case, the number of appearances is within about 1% of the expected value (10,000), so we conclude that the random numbers are probably uniform.

Q-1: If you declare a variable inside a for statement, where can it exist?

• inside of the for loop.
• Correct!
• outside of the for loop, but inside of the function it's used in.
• Incorrect! The variable goes out of scope as soon as the for loop terminates!
• outside of the function, and everywhere else in the program.
• Incorrect! The variable goes out of scope as soon as the for loop terminates!

Q-2: Multiple Response When we increase the size of num_values, which of the following is true?

• the difference between actual and expected number of appearances increases
• Correct! The numbers go from being off by less than 5 to more than 100.
• the difference between actual and expected number of appearances decreases
• Incorrect! Take a look at the numbers again!
• the percent by which the number of appearances differs from the expected number increases
• Incorrect! Take a look at the numbers again!
• the percent by which the number of appearances differs from the expected number decreases
• Incorrect! As we continue to increase the size of num_values, the percent by which the number of appearances differes from the expected value approaches 0.

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