The dean of the School of Data Sciences wishes to know the time spent (hours in a
week) by the CSE students for study purpose. He collects the information from a
random sample of 30 students:
15.0 23.7 19.7 15.4 18.3 23.0 14.2 + δ 20.8 13.5 20.7
17.4 18.6 12.9 + ψ 20.3 13.7 21.4 18.3 29.8 17.1 18.9
10.3 26.1 15.7 14.0 17.8 33.8 23.2 12.9 27.1 16.6    Here, δ is 0 and ψ is 9. Now answer the following question,  Starting with the value 10.0 and considering a class interval of 10, construct a 
frequency distribution (with four columns: class interval (like 10−20, 20−30,...),
tally, frequency, and relative frequency) of time spent for the study purpose.

To construct a frequency distribution for the data provided, we will follow these steps:

1. **Identify the Range and Class Intervals**:  
   - The smallest value in the dataset is 10.3 and the largest is 33.8.
   - The class intervals will start from 10.0 with a width of 10 (as specified).
   - Therefore, the intervals will be: 10−20, 20−30, and 30−40.

2. **Tally the Data**:  
   - We will tally the number of observations that fall into each class interval.

3. **Calculate the Frequency**:  
   - Frequency is the number of data points in each interval.

4. **Calculate the Relative Frequency**:  
   - The relative frequency is calculated by dividing the frequency of each class interval by the total number of observations (which is 30 in this case).

### Data Points
Given the data (with δ = 0 and ψ = 9):
\[ 
\text{Data} = \{15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9+9=21.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6\}
\]

### Frequency Distribution Table

| Class Interval | Tally               | Frequency | Relative Frequency |
|----------------|---------------------|-----------|---------------------|
| 10−20          | |||||||||||||||     | 17        | \( \frac{17}{30} = 0.567 \)|
| 20−30          | |||||||||||||       | 12        | \( \frac{12}{30} = 0.400 \)|
| 30−40          | |                   | 1         | \( \frac{1}{30} = 0.033 \)|

### Explanation:

- **Class Interval (10−20)**: Includes data points from 10.0 to 19.9. 17 students fall into this range.
- **Class Interval (20−30)**: Includes data points from 20.0 to 29.9. 12 students fall into this range.
- **Class Interval (30−40)**: Includes data points from 30.0 to 39.9. Only 1 student falls into this range.

The **Relative Frequency** gives us the proportion of the total number of students that fall into each class interval.

### Summary:

- The majority of students (56.7%) spent between 10 to 20 hours per week studying.
- 40% of students spent between 20 to 30 hours.
- Only 3.3% spent more than 30 hours.

Would you like more details or have any questions?

**Five related questions:**
1. How would the frequency distribution change if the class interval was 5 instead of 10?
2. How can you represent this frequency distribution graphically?
3. What is the cumulative frequency for each class interval?
4. How would you calculate the mean time spent on studying using this frequency distribution?
5. How does the standard deviation of the dataset relate to the class intervals?

**Tip:** When working with frequency distributions, always check if the sum of frequencies matches the total number of observations to ensure accuracy.

The dean of the School of Data Sciences wishes to know the time spent (hours in a week) by the CSE students for study purposes. He collects the information from a random sample of 30 students: 15.0 23.7 19.7 15.4 18.3 23.0 14.2 + δ 20.8 13.5 20.7 17.4 18.6 12.9 + ψ 20.3 13.7 21.4 18.3 29.8 17.1 18.9 10.3 26.1 15.7 14.0 17.8 33.8 23.2 12.9 27.1 16.6. Here, δ is 0 and ψ is 9. Now answer the following question: Starting with the value 10.0 and considering a class interval of 10, construct a frequency distribution (with four columns: class interval (like 10−20, 20−30,...), tally, frequency, and relative frequency) of time spent for the study purpose.

Learn how to construct a frequency distribution table for the time spent studying by CSE students. This problem covers key statistical concepts, including frequency distribution and relative frequency calculation. Suitable for students in Grades 9-12.

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