A sample of students was asked to flip a coin and record their results.  The raw responses are given in this table:
 
Heads

Heads

Tails

Tails

Heads

Tails

Tails

Tails

Heads

Heads

Tails

Heads

Tails

Tails

Heads

Heads

Tails

Tails

Tails

Heads

Heads

Tails

Heads

Heads

Tails

Heads

Heads

Tails

Heads

Heads
 
Give the categorical frequency distribution for these data.

Provide your answer below:

Heads 

Tails

To create a categorical frequency distribution for the given data, we will count the number of times "Heads" and "Tails" appear in the sample.

### Step 1: List the Data
The responses are:
- Heads
- Heads
- Tails
- Tails
- Heads
- Tails
- Tails
- Tails
- Heads
- Heads
- Tails
- Heads
- Tails
- Tails
- Heads
- Heads
- Tails
- Tails
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads

### Step 2: Count the Frequencies
Now, let's count how many times each outcome appears:

| **Outcome** | **Frequency** |
|-------------|---------------|
| Heads       | 16            |
| Tails       | 14            |

### Step 3: Create the Categorical Frequency Distribution

Here is the categorical frequency distribution:

| **Outcome** | **Frequency** |
|-------------|---------------|
| Heads       | 16            |
| Tails       | 14            |

This table shows how often each outcome occurred in the sample of students flipping a coin.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What is the relative frequency of "Heads" and "Tails" in this sample?
2. How would you visualize this frequency distribution using a bar chart?
3. If another student flipped the coin and got "Tails," how would the distribution change?
4. What is the probability of flipping "Heads" based on this sample?
5. How does this distribution compare to the expected 50/50 distribution in a fair coin flip?

**Tip:** When interpreting coin flip results, consider the sample size to assess how closely the data aligns with the expected probability.

Explore the categorical frequency distribution of coin flip results, analyzing how often 'Heads' and 'Tails' appeared in a sample. This problem covers basic statistical analysis and is suitable for Grades 7-9.

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