Sure! Let's analyze the problem step-by-step:
1. Identify Values from the Table:
We categorize students based on their English grades and the number of languages studied.
The table's values are:
- "90 or Above" and "English Only": 15 students
- "Lower than 90" and "English Only": 105 students
- "90 or Above" and "English and Another Language": 110 students
- "Lower than 90" and "English and Another Language": 270 students
2. Calculate Totals for Each Row:
- For the row "English Only":
- Total = 15 (90 or Above) + 105 (Lower than 90) = 120 students
- For the row "English and Another Language":
- Total = 110 (90 or Above) + 270 (Lower than 90) = 380 students
3. Calculate Totals for Each Column:
- For the column "90 or Above":
- Total = 15 (English Only) + 110 (English and Another Language) = 125 students
- For the column "Lower than 90":
- Total = 105 (English Only) + 270 (English and Another Language) = 375 students
4. Calculate Grand Total:
- Total students = Sum of all students, therefore:
- Grand Total = 125 (90 or Above) + 375 (Lower than 90) = 500 students
5. Verify the Table:
Combining all calculations:
[tex]\[
\begin{array}{|r|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & 90\text{ or Above} & \text{Lower than 90} & \text{Total} \\
\hline
\text{English Only} & 15 & 105 & 120 \\
\hline
\begin{array}{c}
\text{English and Another Language}
\end{array} & 110 & 270 & 380 \\
\hline
\text{Total} & 125 & 375 & 500 \\
\hline
\end{array}
\][/tex]
Our calculated values match the given frequency table. Hence, the detailed step-by-step solution confirms that the totals for each category are:
- Total students studying only English: 120
- Total students studying English and another language: 380
- Total students scoring 90 or Above: 125
- Total students scoring Lower than 90: 375
- Grand total number of students: 500
