1. **State the problem:** We have a data set with the following statistics: Mean = 320, Median = 300, Mode = none, Range = 210, Standard Deviation = 70.6. We want to find the new mean, median, mode, range, and standard deviation when each value in the data set is multiplied by 0.5. 2. **Recall the rules for scaling data:** - When each data value is multiplied by a constant $k$, the mean, median, mode, range, and standard deviation are also multiplied by $k$. - The mode remains "none" if there was no mode originally. 3. **Apply the scaling factor $k=0.5$ to each measure:** - New Mean = $0.5 \times 320 = 160$ - New Median = $0.5 \times 300 = 150$ - New Mode = none (unchanged) - New Range = $0.5 \times 210 = 105$ - New Standard Deviation = $0.5 \times 70.6 = 35.3$ 4. **Final answers:** | Measure | New Value | |---------|-----------| | Mean | 160 | | Median | 150 | | Mode | none | | Range | 105 | | Standard Deviation | 35.3 | These results show how multiplying each data point by 0.5 scales all measures of center and dispersion by the same factor, except the mode which remains none.