1. **State the problem:** We have Mikaeel's reading times over 7 days: 35, 30, 39, 35, 35, 22, 42 minutes. We need to find the mean, median, mode, range, check for outliers, and explain dispersion. 2. **Mean time:** The mean is the average time spent reading. Formula: $$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$ Calculate sum: $$35 + 30 + 39 + 35 + 35 + 22 + 42 = 238$$ Number of days = 7 So, $$\text{Mean} = \frac{238}{7} = 34$$ minutes. 3. **Median time:** The median is the middle value when data is ordered. Order the times: 22, 30, 35, 35, 35, 39, 42 Since 7 values, median is the 4th value: 35 minutes. 4. **Modal time:** The mode is the most frequent value. Here, 35 appears 3 times, more than any other number. Mode = 35 minutes. 5. **Range time:** Range is the difference between maximum and minimum values. Max = 42, Min = 22 Range = $$42 - 22 = 20$$ minutes. 6. **Outliers:** Outliers are values significantly different from others. Using the interquartile range (IQR) method: - Q1 (25th percentile) = median of lower half (22, 30, 35) = 30 - Q3 (75th percentile) = median of upper half (35, 39, 42) = 39 - IQR = $$39 - 30 = 9$$ Outlier boundaries: below $$Q1 - 1.5 \times IQR = 30 - 13.5 = 16.5$$ or above $$Q3 + 1.5 \times IQR = 39 + 13.5 = 52.5$$ All values are between 22 and 42, so no outliers. 7. **Dispersion meaning:** Dispersion describes how spread out the data values are. It shows variability or consistency in the data. **Final answers:** - Mean = 34 minutes - Median = 35 minutes - Mode = 35 minutes - Range = 20 minutes - No outliers detected - Dispersion means the spread or variability of data values.