1. **State the problem:** We are given the data set: 90.496, 89.554, 91.393, 86.198, 90.139, 90.496, 86.198, 89.554, 86.198. We need to calculate the mean, median, and mode of this data. 2. **Mean formula:** The mean (average) is calculated by summing all values and dividing by the number of values. $$\text{Mean} = \frac{\sum x_i}{n}$$ 3. **Calculate the mean:** Sum all values: $$90.496 + 89.554 + 91.393 + 86.198 + 90.139 + 90.496 + 86.198 + 89.554 + 86.198 = 800.726$$ Number of values $n = 9$ Mean: $$\frac{800.726}{9} \approx 88.969$$ 4. **Median definition:** The median is the middle value when the data is ordered from smallest to largest. 5. **Order the data:** $$86.198, 86.198, 86.198, 89.554, 89.554, 90.139, 90.496, 90.496, 91.393$$ 6. **Find the median:** Since $n=9$ (odd), median is the value at position $\frac{9+1}{2} = 5$. The 5th value is $89.554$. 7. **Mode definition:** The mode is the value(s) that appear most frequently. 8. **Find the mode:** - $86.198$ appears 3 times - $89.554$ appears 2 times - $90.496$ appears 2 times Mode is $86.198$ because it appears most frequently. **Final answers:** - Mean $\approx 88.969$ - Median $= 89.554$ - Mode $= 86.198$