https://file.aiquickdraw.com/mathbot/file/17253878363666vm42che.jpg

The image you uploaded contains a table showing temperature intervals and their corresponding frequencies, as well as questions related to the data.

### Extracted Information:
- **Temperature (°C):**
  - \(0 \leq T < 5\) : Frequency = 2
  - \(5 \leq T < 10\) : Frequency = 4
  - \(10 \leq T < 15\) : Frequency = 6
  - \(15 \leq T < 20\) : Frequency = 7
  - \(20 \leq T < 25\) : Frequency = 6
  - \(25 \leq T < 30\) : Frequency = 5

The questions are:
1. **Find the modal class interval.**
2. **Calculate an estimate for the mean temperature.**

### Solutions:

#### 1. **Finding the Modal Class Interval**
The modal class interval is the class interval with the highest frequency. From the table, the highest frequency is 7, which corresponds to the interval \(15 \leq T < 20\). 

**Modal class interval: \(15 \leq T < 20\)**

#### 2. **Estimating the Mean Temperature**
To estimate the mean temperature, we can use the midpoints of each class interval and apply the formula for the mean of grouped dataThe image you uploaded contains a table showing temperature intervals and their corresponding frequencies, as well as questions related to the data.

### Extracted Information:
- **Temperature (°C):**
  - \(0 \leq T < 5\) : Frequency = 2
  - \(5 \leq T < 10\) : Frequency = 4
  - \(10 \leq T < 15\) : Frequency = 6
  - \(15 \leq T < 20\) : Frequency = 7
  - \(20 \leq T < 25\) : Frequency = 6
  - \(25 \leq T < 30\) : Frequency = 5

The questions are:
1. **Find the modal class interval.**
2. **Calculate an estimate for the mean temperature.**

### Solutions:

#### 1. **Finding the Modal Class Interval**
The modal class interval is the class interval with the highest frequency. From the table, the highest frequency is 7, which corresponds to the interval \(15 \leq T < 20\). 

**Modal class interval: \(15 \leq T < 20\)**

#### 2. **Estimating the Mean Temperature**
To estimate the mean temperature, we can use the midpoints of each class interval and apply the formula for the mean of grouped 

\[
\text{Estimated Mean} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}}
\]

- **Midpoints:**
  - \(0 \leq T < 5\) : Midpoint = 2.5
  - \(5 \leq T < 10\) : Midpoint = 7.5
  - \(10 \leq T < 15\) : Midpoint = 12.5
  - \(15 \leq T < 20\) : Midpoint = 17.5
  - \(20 \leq T < 25\) : Midpoint = 22.5
  - \(25 \leq T < 30\) : Midpoint = 27.5

- **Calculations:**
  - \(2.5 \times 2 = 5\)
  - \(7.5 \times 4 = 30\)
  - \(12.5 \times 6 = 75\)
  - \(17.5 \times 7 = 122.5\)
  - \(22.5 \times 6 = 135\)
  - \(27.5 \times 5 = 137.5\)

\[
\text{Sum of Midpoint} \times \text{Frequency} = 5 + 30 + 75 + 122.5 + 135 + 137.5 = 505
\]

\[
\text{Sum of Frequencies} = 2 + 4 + 6 + 7 + 6 + 5 = 30
\]

\[
\text{Estimated Mean} = \frac{505}{30} \approx 16.83^\circ \text{C}
\]

**Estimated Mean Temperature: \(16.83^\circ \text{C}\)**

Would you like further details or explanations?

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### Follow-up Questions:

1. How is the median class interval calculated from grouped data?
2. What are the possible sources of error when estimating the mean from grouped data?
3. How does the range of the data set influence the spread of temperatures?
4. What is the significance of the mode in this data set, and how might it be used?
5. If the temperature intervals were smaller, how would that affect the mean estimate?

**Tip:** When estimating the mean from grouped data, remember that smaller class intervals can lead to a more accurate estimate.

The table gives information about the temperature in °C at noon in a town for 50 days. Find the modal class interval and calculate an estimate for the mean temperature for the data in the table.

Learn how to find the modal class interval and estimate the mean temperature from grouped data. The problem involves a frequency distribution table with temperature intervals and requires calculating the mean using midpoints. Suitable for students in Grades 9-11.

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