Show that the total of each column is equal to the total of the sum each row.
20
[tex]\begin{array}{l}
1+3 \\
1+3+6= \\
1+3+6+10+6= \\
\begin{array}{lll}
1+3+6+10+15+10 & = \\
6+15+24+10 & =
\end{array} \\
15+24+10+15+21=
\end{array}[/tex]
Answer:
Answer (1)
Calculate the sum of each row: 1 + 3 = 4 , 1 + 3 + 6 = 10 , 1 + 3 + 6 + 10 + 6 = 26 , 1 + 3 + 6 + 10 + 15 + 10 = 45 , 6 + 15 + 24 + 10 = 55 , 15 + 24 + 10 + 15 + 21 = 85 .
Calculate the total sum of all rows: 4 + 10 + 26 + 45 + 55 + 85 = 225 .
Calculate the sum of each column: 1 + 1 + 1 + 1 + 6 + 15 = 25 , 3 + 3 + 3 + 3 + 15 + 24 = 51 , 6 + 6 + 6 + 6 + 24 + 10 = 58 , 10 + 10 + 10 + 10 + 10 + 15 = 65 , 6 + 15 + 10 + 21 = 52 .
Calculate the total sum of all columns: 25 + 51 + 58 + 65 + 52 = 251 . Since 225 = 251 , the statement is false. F a l se
Explanation
Calculate Row Sums The problem asks us to verify that the sum of each row is equal to the sum of each column in the given table. Let's first calculate the sum of each row.
Calculating Each Row Row 1: 1 + 3 = 4
Row 2: 1 + 3 + 6 = 10
Row 3: 1 + 3 + 6 + 10 + 6 = 26
Row 4: 1 + 3 + 6 + 10 + 15 + 10 = 45
Row 5: 6 + 15 + 24 + 10 = 55
Row 6: 15 + 24 + 10 + 15 + 21 = 85
Total Row Sum Now, let's find the total sum of all rows: 4 + 10 + 26 + 45 + 55 + 85 = 225
Calculating Each Column Next, we need to determine the values in each column and sum them. The columns are implicitly defined by the structure of the table. Column 1: 1 + 1 + 1 + 1 + 6 + 15 = 25 Column 2: 3 + 3 + 3 + 3 + 15 + 24 = 51 Column 3: 6 + 6 + 6 + 6 + 24 + 10 = 58 Column 4: 10 + 10 + 10 + 10 + 10 + 15 = 65 Column 5: 6 + 15 + 10 + 21 = 52
Total Column Sum Now, let's find the total sum of all columns: 25 + 51 + 58 + 65 + 52 = 251
Final Comparison Comparing the total sum of rows (225) and the total sum of columns (251), we see that they are not equal. Therefore, the statement that the total of each row is equal to the total of each column is false.
Conclusion The total sum of the rows is 225, and the total sum of the columns is 251. Since these values are not equal, the initial statement is incorrect.
Examples
In data analysis, verifying the consistency of row and column totals is crucial for ensuring data integrity. For example, if you have a table representing sales data for different products across different regions, the sum of each row (representing a product's total sales) should match the sum of the relevant columns (representing regional sales). If these totals don't match, it indicates an error in the data that needs to be investigated. This principle applies to various fields, including finance, statistics, and engineering, where data accuracy is paramount.
