Question 1194775
I'll start by finding the cumulative frequencies and then proceed to calculate the third quartile, 6th decile, and 80th percentile using the given data.
```python?code_reference&code_event_index=3
import pandas as pd

# Create a DataFrame with the given data
data = {
    'Number of Students Interval': ['16-20', '21-25', '26-30', '31-35', '36-40', '41-45'],
    'Number of Schools': [3, 9, 6, 10, 8, 9]
}
df = pd.DataFrame(data)

# Calculate cumulative frequency
df['Cumulative Frequency'] = df['Number of Schools'].cumsum()

# Calculate Q3, D6, and P80 positions
total_schools = df['Number of Schools'].sum()
Q3_position = (75 / 100) * total_schools
D6_position = (60 / 100) * total_schools
P80_position = (80 / 100) * total_schools

# Function to calculate Q3, D6, and P80
def calculate_quartile_decile_percentile(position):
    for i in range(len(df)):
        if position <= df['Cumulative Frequency'][i]:
            lower_bound = int(df['Number of Students Interval'][i].split('-')[0])
            interval_width = 5
            if i > 0:
                previous_cumulative_frequency = df['Cumulative Frequency'][i - 1]
            else:
                previous_cumulative_frequency = 0
            return lower_bound + ((position - previous_cumulative_frequency) / df['Number of Schools'][i]) * interval_width

# Calculate Q3, D6, and P80
Q3 = calculate_quartile_decile_percentile(Q3_position)
D6 = calculate_quartile_decile_percentile(D6_position)
P80 = calculate_quartile_decile_percentile(P80_position)

# Print the results
print("Q3:", Q3)
print("D6:", D6)
print("P80:", P80)

# Display the first 5 rows
print(df.head().to_markdown(index=False, numalign="left", stralign="left"))

# Print the column names and their data types
print(df.info())
```
```text?code_stdout&code_event_index=3
Q3: 39.59375
D6: 35.5
P80: 41.0
| Number of Students Interval   | Number of Schools   | Cumulative Frequency   |
|:------------------------------|:--------------------|:-----------------------|
| 16-20                         | 3                   | 3                      |
| 21-25                         | 9                   | 12                     |
| 26-30                         | 6                   | 18                     |
| 31-35                         | 10                  | 28                     |
| 36-40                         | 8                   | 36                     |
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 6 entries, 0 to 5
Data columns (total 3 columns):
 #   Column                       Non-Null Count  Dtype 
---  ------                       --------------  ----- 
 0   Number of Students Interval  6 non-null      object
 1   Number of Schools            6 non-null      int64 
 2   Cumulative Frequency         6 non-null      int64 
dtypes: int64(2), object(1)
memory usage: 272.0+ bytes
None

```
The third quartile (Q3) is 39.59, the 6th decile (D6) is 35.5, and the 80th percentile (P80) is 41.0.