Questions: Construct a frequency table for the data Responses Frequency excellent 1 good 2 fair 4 poor 3 Total 10 Construct a relative frequency table for the data. Responses Relative Frequency excellent good fair poor Total (Type integers or decimals)

Solution Steps

To construct a relative frequency table, we need to divide the frequency of each response by the total number of responses. This will give us the relative frequency for each category.

1. Extract the frequencies of each response.
2. Calculate the total number of responses.
3. Divide the frequency of each response by the total number of responses to get the relative frequency.
4. Populate the relative frequency table with these values.

The total number of responses is calculated by summing the frequencies of each category: $$\text{Total} = 1 + 2 + 4 + 3 = 10$$

The relative frequency for each response category is calculated using the formula: $$\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Responses}}$$ Thus, we have:

• For "excellent": $$\text{Relative Frequency}_{\text{excellent}} = \frac{1}{10} = 0.1$$
• For "good": $$\text{Relative Frequency}_{\text{good}} = \frac{2}{10} = 0.2$$
• For "fair": $$\text{Relative Frequency}_{\text{fair}} = \frac{4}{10} = 0.4$$
• For "poor": $$\text{Relative Frequency}_{\text{poor}} = \frac{3}{10} = 0.3$$

The relative frequencies for each response category are:

• Excellent: $0.1$
• Good: $0.2$
• Fair: $0.4$
• Poor: $0.3$

The total of the relative frequencies is: $$\text{Total Relative Frequency} = 0.1 + 0.2 + 0.4 + 0.3 = 1.0$$

Final Answer