Questions: (a) Construct a frequency distribution. Movement Frequency Down 10 No change 3 Up 17 (b) Construct a relative frequency distribution. Movement Relative Frequency Down No change Up (Round to three decimal places as needed.)

Solution Steps

(a) To construct a frequency distribution, we simply list the categories and their corresponding frequencies as given in the table.

(b) To construct a relative frequency distribution, we need to divide the frequency of each category by the total number of observations to get the relative frequency. Then, round the results to three decimal places.

The frequency distribution is constructed by listing the movements along with their corresponding frequencies. The data is as follows:

\[ \begin{array}{|c|c|} \hline \text{Movement} & \text{Frequency} \\ \hline \text{Down} & 10 \\ \hline \text{No change} & 3 \\ \hline \text{Up} & 17 \\ \hline \end{array} \]

To find the total number of observations, we sum the frequencies:

\[ \text{Total Observations} = 10 + 3 + 17 = 30 \]

The relative frequency for each movement is calculated by dividing the frequency of each movement by the total number of observations:

\[ \text{Relative Frequency (Down)} = \frac{10}{30} = 0.333 \] \[ \text{Relative Frequency (No change)} = \frac{3}{30} = 0.1 \] \[ \text{Relative Frequency (Up)} = \frac{17}{30} \approx 0.567 \]

Thus, the relative frequency distribution is:

\[ \begin{array}{|c|c|} \hline \text{Movement} & \text{Relative Frequency} \\ \hline \text{Down} & 0.333 \\ \hline \text{No change} & 0.1 \\ \hline \text{Up} & 0.567 \\ \hline \end{array} \]

Final Answer