Listed below are the exam scores for twenty-five students.
51 63 67 67 68 69 69 70 70 72 73 74 75 75 78 78 80 81 83
85 88 89 89 94 99
a. Construct a frequency distribution using 5 classes and 50 as the first
lower class limit. [7points] the data is 1 6 9 7 2

Let's go step by step to construct a frequency distribution using 5 classes and 50 as the first lower class limit for the given exam scores:

### Step 1: Identify the Range
First, we calculate the range of the dataLet's go step by step to construct a frequency distribution using 5 classes and 50 as the first lower class limit for the given exam scores:

### Step 1: Identify the Range
First, we calculate the range of the 
- **Minimum score** = 51
- **Maximum score** = 99
- **Range** = Maximum - Minimum = 99 - 51 = 48

### Step 2: Determine Class Width
Next, we calculate the class width by dividing the range by the number of classes (which is 5):
- **Class width** = \( \frac{48}{5} = 9.6 \)
  - We round up to the nearest whole number, so the class width becomes **10**.

### Step 3: Set Class Limits
We start with 50 as the first lower class limit. Using the class width of 10, the class limits will be:

1. 50 - 59
2. 60 - 69
3. 70 - 79
4. 80 - 89
5. 90 - 99

### Step 4: Tally the Data
Now, we tally the number of data points in each class.

| **Class Interval** | **Tally** | **Frequency** |
|--------------------|-----------|---------------|
| 50 - 59            | 51        | 1             |
| 60 - 69            | 63, 67, 67, 68, 69, 69   | 6             |
| 70 - 79            | 70, 70, 72, 73, 74, 75, 75, 78, 78 | 9             |
| 80 - 89            | 80, 81, 83, 85, 88, 89, 89 | 7             |
| 90 - 99            | 94, 99    | 2             |

### Step 5: Construct the Frequency Distribution Table

| **Class Interval** | **Frequency** |
|--------------------|---------------|
| 50 - 59            | 1             |
| 60 - 69            | 6             |
| 70 - 79            | 9             |
| 80 - 89            | 7             |
| 90 - 99            | 2             |

This is the frequency distribution for the given data.

Would you like more details on this, or any clarification?

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Here are 5 related questions to deepen understanding:
1. How would you calculate relative frequency for each class?
2. What is the cumulative frequency distribution for this data?
3. How would you create a histogram based on this frequency distribution?
4. How does changing the number of classes affect the frequency distribution?
5. How do you interpret skewness in the frequency distribution?

**Tip:** When determining class width, always round up the calculated width to ensure all data is included in the intervals.

Listed below are the exam scores for twenty-five students. 51 63 67 67 68 69 69 70 70 72 73 74 75 75 78 78 80 81 83 85 88 89 89 94 99 a. Construct a frequency distribution using 5 classes and 50 as the first lower class limit.

Learn how to construct a frequency distribution with 5 classes using exam scores from 25 students. The first lower class limit is set at 50, and key statistical concepts such as range, class width, and tallying are covered. This detailed guide is suitable for students in Grades 9-12.

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