SOLUTION: The table shows a distribution for the number of top performing students in mathematics in 45 schools in the Cordillera Region. Calculate the third quartile (Q3), 6th decile (D6),

Question 1194775: The table shows a distribution for the number of top performing students in mathematics in 45 schools in the Cordillera Region. Calculate the third quartile (Q3), 6th decile (D6), and the 80th percentile (P80) of the number of students given the number of schools.
Number of Students Interval Number of Schools
16-20 3
21-25 9
26-30 6
31-35 10
36-40 8
41-45 9
Answer by proyaop(69) (Show Source): You can put this solution on YOUR website!
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 |

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.
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