1. **State the problem:** Raina's bowling scores are 107, 130, 136, 140, 140, 142, 144, 167. We want to see how changing the score 142 to 156 affects the range and the interquartile range (IQR). 2. **Recall formulas:** - Range = maximum value - minimum value - IQR = Q3 - Q1, where Q1 is the first quartile and Q3 is the third quartile 3. **Original data:** 107, 130, 136, 140, 140, 142, 144, 167 - Minimum = 107 - Maximum = 167 - Range = 167 - 107 = 60 4. **Find quartiles for original data:** - Number of data points $n=8$ - Median is average of 4th and 5th values: $\frac{140 + 140}{2} = 140$ - Lower half: 107, 130, 136, 140 - Upper half: 140, 142, 144, 167 - Q1 is median of lower half: $\frac{130 + 136}{2} = 133$ - Q3 is median of upper half: $\frac{142 + 144}{2} = 143$ - IQR = $143 - 133 = 10$ 5. **Change 142 to 156 and reorder:** 107, 130, 136, 140, 140, 144, 156, 167 - Minimum = 107 - Maximum = 167 - Range = $167 - 107 = 60$ 6. **Find quartiles for new data:** - Median is average of 4th and 5th values: $\frac{140 + 140}{2} = 140$ - Lower half: 107, 130, 136, 140 - Upper half: 144, 156, 167 - Q1 is median of lower half: $\frac{130 + 136}{2} = 133$ - Q3 is median of upper half: median of 144, 156, 167 is 156 - IQR = $156 - 133 = 23$ 7. **Compare range:** - Original range = 60 - New range = 60 - Range stays the same. 8. **Compare IQR:** - Original IQR = 10 - New IQR = 23 - IQR increases by $23 - 10 = 13$ points. **Final answers:** - (a) The range stays the same. - (b) The IQR increases by 13 points.