Certainly! Let's create a histogram step-by-step to represent the given frequency table.
A histogram is a type of bar graph that represents the frequency of various outcomes in a dataset. Here’s how we can create one for the given data:
### Step-by-Step Solution
1. Identify the Data:
- Values: 3, 4, 5, 6, 7, 8
- Frequencies: 8, 4, 3, 2, 2, 7
2. Prepare the Axes:
- The horizontal axis (x-axis) will represent the values.
- The vertical axis (y-axis) will represent the frequencies.
3. Draw the Bars:
- For the value 3, draw a bar that reaches up to 8 on the y-axis.
- For the value 4, draw a bar that reaches up to 4 on the y-axis.
- For the value 5, draw a bar that reaches up to 3 on the y-axis.
- For the value 6, draw a bar that reaches up to 2 on the y-axis.
- For the value 7, draw a bar that reaches up to 2 on the y-axis.
- For the value 8, draw a bar that reaches up to 7 on the y-axis.
4. Label the Axes:
- Label the x-axis as "Value".
- Label the y-axis as "Frequency".
5. Add Title:
- Add a title to your histogram, such as "Histogram of Values".
Using this information, you can draw the histogram manually or use a tool to create it. Below is a description of what the histogram looks like:
- Bar for Value 3: Tall bar reaching up to 8
- Bar for Value 4: Bar reaching up to 4
- Bar for Value 5: Bar reaching up to 3
- Bar for Value 6: Bar reaching up to 2
- Bar for Value 7: Bar reaching up to 2
- Bar for Value 8: Tall bar reaching up to 7
### Visual Representation:
Here's a rough sketch of what the histogram would look like:
```
Frequency
9 |
8 | [ ][ ][ ][ ][ ][ ][ ][ ]
7 | [ ][ ][ ][ ][ ][ ][ ]
6 |
5 |
4 | [ ][ ][ ][ ]
3 | [ ][ ][ ]
2 | [ ][ ] [ ][ ]
1 |
------------------------------------------------
3 4 5 6 7 8
Value
```
Each bracket `[ ]` represents a unit of frequency and their alignment on the horizontal axis represents the values.
By following these steps, you can construct an accurate histogram from the provided frequency table.
