The number of stories in each of a sample of the world’s 20 tallest buildings follows. Construct a grouped frequency distribution and a cumulative frequency distribution with 9 classes.

55	80	70	79	54	56	78	77	64	60
71	55	60	75	55	69	65	75	70	72

To construct a grouped frequency distribution and a cumulative frequency distribution for the number of stories in these buildings, we follow these steps:

### 1. **Identify the Range:**
   - The minimum number of stories is 54, and the maximum is 80.
   - Range = Maximum - Minimum = \( 80 - 54 = 26 \)

### 2. **Determine the Class Width:**
   - Number of classes = 9 (as specified).
   - Class width = \( \frac{\text{Range}}{\text{Number of Classes}} \)
   - \( \frac{26}{9} \approx 2.89 \), rounded up to 3.

### 3. **Create Class Intervals:**
   The class intervals will start from the minimum value (54) and add the class width (3) to create 9 classes.

| Class Interval | Frequency |
|----------------|-----------|
| 54 - 56        |     4     |
| 57 - 59        |     0     |
| 60 - 62        |     3     |
| 63 - 65        |     2     |
| 66 - 68        |     0     |
| 69 - 71        |     3     |
| 72 - 74        |     2     |
| 75 - 77        |     4     |
| 78 - 80        |     2     |

### 4. **Cumulative Frequency Distribution:**

| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 54 - 56        |     4     |          4           |
| 57 - 59        |     0     |          4           |
| 60 - 62        |     3     |          7           |
| 63 - 65        |     2     |          9           |
| 66 - 68        |     0     |          9           |
| 69 - 71        |     3     |          12          |
| 72 - 74        |     2     |          14          |
| 75 - 77        |     4     |          18          |
| 78 - 80        |     2     |          20          |

The cumulative frequency column shows the total number of buildings up to and including each class interval.

### Summary:
- Class width: 3
- Number of classes: 9
- Cumulative frequency shows how data accumulates across intervals.

Would you like any more details, or have any questions?

Here are 5 related questions you might find interesting:
1. How does changing the class width affect the distribution?
2. What is the relative frequency for each class?
3. Can we determine the mode from the grouped frequency distribution?
4. How would this distribution change if a 21st building were added?
5. How can this data be used to analyze trends in skyscraper heights?

**Tip:** When constructing frequency distributions, always round up the class width to ensure that all data points are included within the range.

The number of stories in each of a sample of the world’s 20 tallest buildings follows. Construct a grouped frequency distribution and a cumulative frequency distribution with 9 classes.

Learn how to construct a grouped frequency distribution and a cumulative frequency distribution for the number of stories in 20 of the world's tallest buildings, with 9 classes. This problem covers key statistical concepts such as class intervals, frequency, and cumulative frequency. Suitable for students in Grades 10-12.

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