1. **Problem:** Find the mean attendance of 10 students in the hostel using the short method. 2. **Given data:** Attendance = 21, 15, 16, 18, 14, 17, 15, 12, 13, 11 3. **Formula for mean by short method:** $$\bar{x} = a + \frac{\sum d}{n}$$ where $a$ is the assumed mean, $d = x_i - a$, and $n$ is the number of observations. 4. **Step 1:** Choose an assumed mean $a$. Let's take $a = 15$ (a value near the middle). 5. **Step 2:** Calculate deviations $d = x_i - 15$: - 21 - 15 = 6 - 15 - 15 = 0 - 16 - 15 = 1 - 18 - 15 = 3 - 14 - 15 = -1 - 17 - 15 = 2 - 15 - 15 = 0 - 12 - 15 = -3 - 13 - 15 = -2 - 11 - 15 = -4 6. **Step 3:** Sum of deviations: $$\sum d = 6 + 0 + 1 + 3 - 1 + 2 + 0 - 3 - 2 - 4 = 2$$ 7. **Step 4:** Number of observations $n = 10$. 8. **Step 5:** Calculate mean: $$\bar{x} = 15 + \frac{2}{10} = 15 + 0.2 = 15.2$$ **Final answer:** The mean attendance is $15.2$.