To draw a histogram for the given data and specified intervals, we need to follow these steps:
1. Collect the Given Data:
- The data is: 8, 9, 5, 14, 5, 14, 15, 7, 13, 6, 4, 10, 6, 6, 7, 5, 5, 12, 9, 8
2. Define the Intervals:
- The intervals are: [tex]\( 4-6 \)[/tex], [tex]\( 7-9 \)[/tex], [tex]\( 10-12 \)[/tex], [tex]\( 13-15 \)[/tex]
3. Determine the Frequency of Each Interval:
- Count how many data points fall into each interval:
- [tex]\( 4-6 \)[/tex]:
- Data points: 5, 5, 5, 6, 6, 4, 6, 6
- Frequency: 8
- [tex]\( 7-9 \)[/tex]:
- Data points: 8, 9, 7, 9, 8, 7
- Frequency: 6
- [tex]\( 10-12 \)[/tex]:
- Data points: 10, 12
- Frequency: 2
- [tex]\( 13-15 \)[/tex]:
- Data points: 14, 14, 15, 13
- Frequency: 4
4. Draw the Histogram:
- We will create a histogram with the x-axis representing the intervals and the y-axis representing the frequencies.
5. Step-by-Step Construction:
- On the x-axis, mark the intervals: [tex]\( 4-6 \)[/tex], [tex]\( 7-9 \)[/tex], [tex]\( 10-12 \)[/tex], [tex]\( 13-15 \)[/tex]
- On the y-axis, mark the frequencies (0 to 8)
- Draw bars corresponding to the frequency of each interval.
Here is the detailed histogram:
```
Frequency
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
+---------------------------------------------
4-6 7-9 10-12 13-15
```
- The bar for interval [tex]\( 4-6 \)[/tex] reaches up to 8.
- The bar for interval [tex]\( 7-9 \)[/tex] reaches up to 6.
- The bar for interval [tex]\( 10-12 \)[/tex] reaches up to 2.
- The bar for interval [tex]\( 13-15 \)[/tex] reaches up to 4.
Make sure your drawn histogram properly follows the same structure, showing the frequencies for each given interval accurately.
