document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "Number of Students Interval Number of Schools
\n" ); document.write( "16-20 3
\n" ); document.write( "21-25 9
\n" ); document.write( "26-30 6
\n" ); document.write( "31-35 10
\n" ); document.write( "36-40 8
\n" ); document.write( "41-45 9
\n" ); document.write( "

Algebra.Com's Answer #848502 by proyaop(69)\"\" \"About 
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.
\n" ); document.write( "```python?code_reference&code_event_index=3
\n" ); document.write( "import pandas as pd\r
\n" ); document.write( "\n" ); document.write( "# Create a DataFrame with the given data
\n" ); document.write( "data = {
\n" ); document.write( " 'Number of Students Interval': ['16-20', '21-25', '26-30', '31-35', '36-40', '41-45'],
\n" ); document.write( " 'Number of Schools': [3, 9, 6, 10, 8, 9]
\n" ); document.write( "}
\n" ); document.write( "df = pd.DataFrame(data)\r
\n" ); document.write( "\n" ); document.write( "# Calculate cumulative frequency
\n" ); document.write( "df['Cumulative Frequency'] = df['Number of Schools'].cumsum()\r
\n" ); document.write( "\n" ); document.write( "# Calculate Q3, D6, and P80 positions
\n" ); document.write( "total_schools = df['Number of Schools'].sum()
\n" ); document.write( "Q3_position = (75 / 100) * total_schools
\n" ); document.write( "D6_position = (60 / 100) * total_schools
\n" ); document.write( "P80_position = (80 / 100) * total_schools\r
\n" ); document.write( "\n" ); document.write( "# Function to calculate Q3, D6, and P80
\n" ); document.write( "def calculate_quartile_decile_percentile(position):
\n" ); document.write( " for i in range(len(df)):
\n" ); document.write( " if position <= df['Cumulative Frequency'][i]:
\n" ); document.write( " lower_bound = int(df['Number of Students Interval'][i].split('-')[0])
\n" ); document.write( " interval_width = 5
\n" ); document.write( " if i > 0:
\n" ); document.write( " previous_cumulative_frequency = df['Cumulative Frequency'][i - 1]
\n" ); document.write( " else:
\n" ); document.write( " previous_cumulative_frequency = 0
\n" ); document.write( " return lower_bound + ((position - previous_cumulative_frequency) / df['Number of Schools'][i]) * interval_width\r
\n" ); document.write( "\n" ); document.write( "# Calculate Q3, D6, and P80
\n" ); document.write( "Q3 = calculate_quartile_decile_percentile(Q3_position)
\n" ); document.write( "D6 = calculate_quartile_decile_percentile(D6_position)
\n" ); document.write( "P80 = calculate_quartile_decile_percentile(P80_position)\r
\n" ); document.write( "\n" ); document.write( "# Print the results
\n" ); document.write( "print(\"Q3:\", Q3)
\n" ); document.write( "print(\"D6:\", D6)
\n" ); document.write( "print(\"P80:\", P80)\r
\n" ); document.write( "\n" ); document.write( "# Display the first 5 rows
\n" ); document.write( "print(df.head().to_markdown(index=False, numalign=\"left\", stralign=\"left\"))\r
\n" ); document.write( "\n" ); document.write( "# Print the column names and their data types
\n" ); document.write( "print(df.info())
\n" ); document.write( "```
\n" ); document.write( "```text?code_stdout&code_event_index=3
\n" ); document.write( "Q3: 39.59375
\n" ); document.write( "D6: 35.5
\n" ); document.write( "P80: 41.0
\n" ); document.write( "| Number of Students Interval | Number of Schools | Cumulative Frequency |
\n" ); document.write( "|:------------------------------|:--------------------|:-----------------------|
\n" ); document.write( "| 16-20 | 3 | 3 |
\n" ); document.write( "| 21-25 | 9 | 12 |
\n" ); document.write( "| 26-30 | 6 | 18 |
\n" ); document.write( "| 31-35 | 10 | 28 |
\n" ); document.write( "| 36-40 | 8 | 36 |
\n" ); document.write( "
\n" ); document.write( "RangeIndex: 6 entries, 0 to 5
\n" ); document.write( "Data columns (total 3 columns):
\n" ); document.write( " # Column Non-Null Count Dtype
\n" ); document.write( "--- ------ -------------- -----
\n" ); document.write( " 0 Number of Students Interval 6 non-null object
\n" ); document.write( " 1 Number of Schools 6 non-null int64
\n" ); document.write( " 2 Cumulative Frequency 6 non-null int64
\n" ); document.write( "dtypes: int64(2), object(1)
\n" ); document.write( "memory usage: 272.0+ bytes
\n" ); document.write( "None\r
\n" ); document.write( "\n" ); document.write( "```
\n" ); document.write( "The third quartile (Q3) is 39.59, the 6th decile (D6) is 35.5, and the 80th percentile (P80) is 41.0.
\n" ); document.write( "
\n" );