1. **Stating the problem:** We are given a frequency distribution with class intervals, real limits, frequencies, and relative frequencies. We want to understand how to calculate the class interval width and the class mark (midpoint) for grouped data. 2. **Formula for class interval width:** The class interval width $i$ is calculated as: $$i = \frac{\text{Highest value} - \text{Lowest value}}{\text{Number of class intervals}}$$ 3. **Given data:** - Highest value = 100 - Lowest value = 37 - Number of class intervals = 10 4. **Calculate the range:** $$\text{Range} = 100 - 37 = 63$$ 5. **Calculate class interval width:** $$i = \frac{63}{10} = 6.3 \approx 6$$ 6. **Class intervals example:** The class intervals are given as 95-100, 89-94, 83-88, etc., each approximately 6 units wide. 7. **Real limits:** Real limits extend the class intervals by 0.5 on each side, e.g., 94.5-100.5 for 95-100. 8. **Class mark (midpoint) calculation:** For a class interval $a-b$, the class mark $x_m$ is: $$x_m = \frac{a + b}{2}$$ Example for 95-100: $$x_m = \frac{95 + 100}{2} = 97.5$$ 9. **Relative frequency:** Relative frequency is the frequency of a class divided by the total number of observations. 10. **Summary:** - Range = 63 - Class interval width $i \approx 6$ - Real limits extend intervals by 0.5 - Class marks are midpoints of intervals This helps organize data for frequency distribution and histogram plotting.