1. **State the problem:** We have the data set 4, 6, 2, 5, 8, 1, 3. We want to find which measure of central tendency (mean, median, mode, or range) remains the same if the 1 is changed to a 2. 2. **Original data:** 4, 6, 2, 5, 8, 1, 3 3. **New data:** 4, 6, 2, 5, 8, 2, 3 4. **Calculate the mean:** - Original mean: $$\frac{4+6+2+5+8+1+3}{7} = \frac{29}{7} \approx 4.14$$ - New mean: $$\frac{4+6+2+5+8+2+3}{7} = \frac{30}{7} \approx 4.29$$ - The mean changes. 5. **Calculate the median:** - Sort original data: 1, 2, 3, 4, 5, 6, 8 - Median is the middle value (4th value): 4 - Sort new data: 2, 2, 3, 4, 5, 6, 8 - Median is still the 4th value: 4 - The median remains the same. 6. **Calculate the mode:** - Original data: all values appear once, no mode. - New data: 2 appears twice, mode is 2. - The mode changes. 7. **Calculate the range:** - Original range: max - min = 8 - 1 = 7 - New range: max - min = 8 - 2 = 6 - The range changes. **Final answer:** The measure of central tendency that remains the same is the **median**.