Making a good histogram from raw data is an important skill in statistics, especially for Year 12 students studying at the AS-Level. A histogram helps you see how numbers distribute, making it easier to find trends and patterns. Here’s a simple guide to help you create one:

Step 1: Gather Your Data

First, collect your raw data. For example, let’s look at the ages of 15 students:

14, 15, 14, 16, 18, 17, 15, 14, 20, 21, 19, 18, 16, 17, 19

Step 2: Determine the Range

Next, you need to find out the range of your data. You do this by subtracting the smallest number from the biggest number. In our example, the smallest age is 14 and the biggest is 21. So, the range is:

$$\text{Range} = 21 - 14 = 7$$

Step 3: Choose the Number of Bins

Now, decide how many bins (or groups) you want to use. A good rule is to take the square root of the number of data points. We have 15 data points, so:

$$\text{Number of bins} \approx \sqrt{15} \approx 4$$

Step 4: Determine Bin Width

Now, let’s figure out how wide each bin should be. You can do this by dividing the range by the number of bins:

$$\text{Bin Width} = \frac{\text{Range}}{\text{Number of bins}} = \frac{7}{4} \approx 1.75$$

You can round this to a simpler number, like 2.

Step 5: Define the Bins

Using the rounded width, set up your bins. For our data, we can create the following bins:

• 14 - 15
• 16 - 17
• 18 - 19
• 20 - 21

Step 6: Tally and Count Frequencies

Now, count how many data points are in each bin:

• 14 - 15: 5 (14, 14, 14, 15, 15)
• 16 - 17: 4 (16, 16, 17, 17)
• 18 - 19: 3 (18, 18, 19, 19)
• 20 - 21: 3 (20, 21)

Step 7: Draw the Histogram

Finally, you’re ready to draw your histogram! You can use graph paper or software.

1. X-axis: Mark your bins (14-15, 16-17, etc.).
2. Y-axis: Mark the number of counts.
3. Draw bars for each bin. The height of each bar should match the number of counts.

Step 8: Interpret Your Histogram

Now, take a look at your histogram. Look for patterns, like the shape of the graph (is it uniform, bell-shaped, etc.) and check for any unusual points (outliers). This helps you understand your data better.

By following these steps, you will create a clear and useful histogram that will help you make sense of your raw data!