1. **State the problem:** We have a data set with mean = 15, median = 13, mode = 9, range = 22, and standard deviation = 4. We apply the function $$y = 2x + 6$$ to each value in the data set and want to find the new mean, median, mode, range, and standard deviation. 2. **Recall formulas and rules:** - When applying a linear transformation $$y = a x + b$$ to data: - New mean $$= a \times \text{old mean} + b$$ - New median $$= a \times \text{old median} + b$$ - New mode $$= a \times \text{old mode} + b$$ - New range $$= a \times \text{old range}$$ (range shifts by $$b$$ but since range is difference, $$b$$ cancels out) - New standard deviation $$= |a| \times \text{old standard deviation}$$ (standard deviation is scaled by $$|a|$$, translation $$b$$ does not affect it) 3. **Calculate each measure:** - Mean: $$2 \times 15 + 6 = 30 + 6 = 36$$ - Median: $$2 \times 13 + 6 = 26 + 6 = 32$$ - Mode: $$2 \times 9 + 6 = 18 + 6 = 24$$ - Range: $$2 \times 22 = 44$$ - Standard deviation: $$|2| \times 4 = 8$$ 4. **Final answer:** Mean = 36, Median = 32, Mode = 24, Range = 44, Standard Deviation = 8