Calculate and solve give it in tabular form

To calculate and solve the problem based on the provided table, I will perform the following steps:

1. **Marginal Totals:** Calculate the sum of each row and each column.
2. **Overall Total:** Sum of all the values in the table.
3. **Row and Column Means:** Calculate the mean for each row and column.
4. **Grand Mean:** Calculate the overall mean of all data points.

### Steps:

1. **Extract Data from the Table**: I will first extract the numerical values from the table.
2. **Calculate Row Totals and Column Totals**: Sum the values for each row and each column.
3. **Calculate the Overall Total and Mean**: Sum all the values and divide by the total number of entries.
4. **Present Results in a New Table**: Show the results in an extended table format.

Let me proceed with these calculations.

### Extracted Data:
From the image, the table data is:

|    | T1  | T2  | T3  | T4  | T5  | T6  |
|----|-----|-----|-----|-----|-----|-----|
| R1 |  6  |  9  |  8  | 14  |  11 |  7  |
| R2 | 10  |  7  |  6  | 15  |  9  |  10 |
| R3 | 12  | 11  | 15  | 13  | 10  |  7  |
| R4 | 11  | 15  | 14  | 13  | 15  | 12  |
| R5 |  7  |  8  | 10  | 12  | 11  | 9   |
| R6 | 10  | 14  | 12  | 15  | 14  | 13  |

### 1. **Calculating Row and Column Totals:**

#### Row Totals:
- \( R1 = 6 + 9 + 8 + 14 + 11 + 7 = 55 \)
- \( R2 = 10 + 7 + 6 + 15 + 9 + 10 = 57 \)
- \( R3 = 12 + 11 + 15 + 13 + 10 + 7 = 68 \)
- \( R4 = 11 + 15 + 14 + 13 + 15 + 12 = 80 \)
- \( R5 = 7 + 8 + 10 + 12 + 11 + 9 = 57 \)
- \( R6 = 10 + 14 + 12 + 15 + 14 + 13 = 78 \)

#### Column Totals:
- \( T1 = 6 + 10 + 12 + 11 + 7 + 10 = 56 \)
- \( T2 = 9 + 7 + 11 + 15 + 8 + 14 = 64 \)
- \( T3 = 8 + 6 + 15 + 14 + 10 + 12 = 65 \)
- \( T4 = 14 + 15 + 13 + 13 + 12 + 15 = 82 \)
- \( T5 = 11 + 9 + 10 + 15 + 11 + 14 = 70 \)
- \( T6 = 7 + 10 + 7 + 12 + 9 + 13 = 58 \)

#### Overall Total:
- \( \text{Overall Total} = 55 + 57 + 68 + 80 + 57 + 78 = 395 \)

### 2. **Calculate Row and Column Means:**

#### Row Means:
- \( \text{Mean of R1} = \frac{55}{6} = 9.17 \)
- \( \text{Mean of R2} = \frac{57}{6} = 9.50 \)
- \( \text{Mean of R3} = \frac{68}{6} = 11.33 \)
- \( \text{Mean of R4} = \frac{80}{6} = 13.33 \)
- \( \text{Mean of R5} = \frac{57}{6} = 9.50 \)
- \( \text{Mean of R6} = \frac{78}{6} = 13.00 \)

#### Column Means:
- \( \text{Mean of T1} = \frac{56}{6} = 9.33 \)
- \( \text{Mean of T2} = \frac{64}{6} = 10.67 \)
- \( \text{Mean of T3} = \frac{65}{6} = 10.83 \)
- \( \text{Mean of T4} = \frac{82}{6} = 13.67 \)
- \( \text{Mean of T5} = \frac{70}{6} = 11.67 \)
- \( \text{Mean of T6} = \frac{58}{6} = 9.67 \)

### 3. **Final Extended Table with Totals and Means:**

|    | T1  | T2  | T3  | T4  | T5  | T6  | **Row Totals** | **Row Means**  |
|----|-----|-----|-----|-----|-----|-----|---------------|----------------|
| R1 |  6  |  9  |  8  | 14  |  11 |  7  |      55       |     9.17       |
| R2 | 10  |  7  |  6  | 15  |  9  |  10 |      57       |     9.50       |
| R3 | 12  | 11  | 15  | 13  | 10  |  7  |      68       |     11.33      |
| R4 | 11  | 15  | 14  | 13  | 15  | 12  |      80       |     13.33      |
| R5 |  7  |  8  | 10  | 12  | 11  |  9  |      57       |     9.50       |
| R6 | 10  | 14  | 12  | 15  | 14  | 13  |      78       |     13.00      |
| **Column Totals** | **56** | **64** | **65** | **82** | **70** | **58** | **Overall Total = 395** |  **Overall Mean = 10.97** |
| **Column Means**  | 9.33 | 10.67 | 10.83 | 13.67 | 11.67 | 9.67 |               |                |

This table summarizes all the totals and means for each row and column, along with the overall total and mean.

Would you like to explore any specific analysis or have any questions about these calculations?

Here are five questions you might consider:
1.

Learn how to calculate and solve tabular data with a step-by-step analysis. This problem involves statistical analysis, including calculating row and column totals, means, and overall totals. Suitable for high school and above.

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