To calculate column percentages and row percentages, let's break it down step-by-step based on the table you provided:

Table Structure Recap:

The table has data categorized by Eye color (Green, Blue, Black) and Gender (Male, Female), with total rows and columns summing up the values.

Let's summarize the table's values:

Now, let's explain how to calculate column and row percentages.

1. Column Percentage:

The column percentage is calculated as the proportion of each cell's value relative to the total for that column. For each value in the column (e.g., Male or Female), divide the cell value by the total of that column.

Formula:

$\text{Column Percentage} = \frac{\text{Cell Value}}{\text{Column Total}} \times 100$

Example (Column: Male):

For Green (Male): $\frac{1}{8} \times 100 = 12.5\%$

For Blue (Male): $\frac{2}{8} \times 100 = 25\%$

For Black (Male): $\frac{5}{8} \times 100 = 62.5\%$

We do the same for the Female column:

• Green (Female) = $\frac{8}{24} \times 100 = 33.33\%$
• Blue (Female) = $\frac{7}{24} \times 100 = 29.17\%$
• Black (Female) = $\frac{9}{24} \times 100 = 37.5\%$

2. Row Percentage:

The row percentage is calculated as the proportion of each cell's value relative to the total for that row. For each value in the row (e.g., Green, Blue, or Black), divide the cell value by the total of that row.

Formula:

$\text{Row Percentage} = \frac{\text{Cell Value}}{\text{Row Total}} \times 100$

Example (Row: Green):

For Male (Green): $\frac{1}{9} \times 100 = 11.11\%$

For Female (Green): $\frac{8}{9} \times 100 = 88.89\%$

We do the same for other rows:

• Blue (Male) = $\frac{2}{9} \times 100 = 22.22\%$
• Blue (Female) = $\frac{7}{9} \times 100 = 77.78\%$
• Black (Male) = $\frac{5}{14} \times 100 = 35.71\%$
• Black (Female) = $\frac{9}{14} \times 100 = 64.29\%$

Summary of Results:

Column Percentages:

• Male: Green 12.5%, Blue 25%, Black 62.5%
• Female: Green 33.33%, Blue 29.17%, Black 37.5%

Row Percentages:

• Green: Male 11.11%, Female 88.89%
• Blue: Male 22.22%, Female 77.78%
• Black: Male 35.71%, Female 64.29%

Would you like more details or further clarification?

Follow-up questions:

1. How would you calculate the total percentage contribution of a specific gender across all rows?
2. Can column and row percentages be used to infer any trends in eye color preferences based on gender?
3. What are the key differences between calculating column vs. row percentages?
4. How would you calculate the percentage of the entire population represented by one gender with a specific eye color?
5. How can these percentages help in making predictions or understanding patterns in a different dataset?

Tip:

Always ensure that the column and row totals match the individual cell contributions to avoid errors when calculating percentages!