Question

Question Completion Status:
Question 1

Consider the following data:

19 10 9 8 14 11 11 12 11 9 19 19

17 10 13 18 16 17 5 14 11 15 18 12

8 7 10 16 2 12

Construct a frequency distribution by making the class width 3 and the lower limit of the first class 2.



Intervals / Intervalle Class Midpoints / Klasmiddelpunte Frequencies / Frekwensies Cumulative frequency / Kumulatiewe frekwensies Relative frequency / Relatiewe frekwensie
[ - )
[ A - ) D H J
[ - ) F
[ - B ) K
[ - ) E I
[ - ) G
Total C


What is the value of G in the table?

Answer 1

To create a frequency distribution table with a class width of 3 and the lower limit of the first class starting at 2, we can first identify the intervals and then count how many data points fall into each interval.

Here’s the breakdown of the intervals:

1. **[2 - 5)**: Includes numbers 2, 3, 4 (but not 5)
2. **[5 - 8)**: Includes numbers 5, 6, 7, 8 (not including 8)
3. **[8 - 11)**: Includes numbers 8, 9, 10, 11 (not including 11)
4. **[11 - 14)**: Includes 11, 12, 13 (not including 14)
5. **[14 - 17)**: Includes 14, 15, 16 (not including 17)
6. **[17 - 20)**: Includes 17, 18, 19 (not including 20)

Now we will count how many numbers fall into each of these intervals based on the given data.

### Data points:
```
19, 10, 9, 8, 14, 11, 11, 12, 11, 9, 19, 19
17, 10, 13, 18, 16, 17, 5, 14, 11, 15, 18, 12
8, 7, 10, 16, 2, 12
```
### Counts per interval:
- **[2 - 5)**: **1** (number 2)
- **[5 - 8)**: **1** (number 5)
- **[8 - 11)**: **6** (numbers: 8, 9, 9, 10, 10, 11, 11, 11)
- **[11 - 14)**: **7** (numbers: 11, 11, 12, 12, 13)
- **[14 - 17)**: **5** (numbers: 14, 14, 15, 16, 16)
- **[17 - 20)**: **6** (numbers: 17, 17, 18, 18, 19, 19, 19)

### Now, compiling this into the frequency distribution table:
| Intervals | Class Midpoints | Frequencies | Cumulative Frequency | Relative Frequency |
|------------------|----------------|-------------|----------------------|--------------------|
| [2 - 5) | 3.5 | 1 | 1 | 1/30 (0.0333) |
| [5 - 8) | 6.5 | 1 | 2 | 1/30 (0.0333) |
| [8 - 11) | 9.5 | 6 | 8 | 6/30 (0.2) |
| [11 - 14) | 12.5 | 7 | 15 | 7/30 (0.2333) |
| [14 - 17) | 15.5 | 5 | 20 | 5/30 (0.1667) |
| [17 - 20) | 18.5 | 6 | 26 | 6/30 (0.2) |
| **Total** | | **30** | | **1** |

From the frequency counts, we can see that the frequency in the interval [17 - 20) is **6**, so the value of **G** is **6**.

Therefore, **G = 6**.