Answer
* Although the **mean attitude score remained unchanged** at **5.0**, the **standard deviation increased dramatically** from **1.20** (before) to **3.78** (after).
* This suggests that **students’ responses became much more polarized** after the poetry unit—some grew significantly more favorable toward poetry, while others became more negative.
* The teacher's disappointment in the mean change being zero overlooks a key insight: the **variance in attitudes increased**, implying that the unit had a substantial impact, but in **divergent** directions.
Work Step by Step
### **Scores**
* **Before**: 7, 5, 3, 5, 5, 4, 5, 6
* **After**: 9, 8, 2, 1, 8, 9, 1, 2
* $N = 8$ (for both)
---
## **Before Scores**
$$
\bar{X}_{\text{before}} = \frac{7 + 5 + 3 + 5 + 5 + 4 + 5 + 6}{8} = \frac{40}{8} = 5.0
$$
$$
s^2 = \frac{\sum (X - \bar{X})^2}{N - 1} = \frac{10}{7} \approx 1.43
$$
$$
s = \sqrt{1.43} \approx 1.20
$$
---
## **After Scores**
$$
\bar{X}_{\text{after}} = \frac{9 + 8 + 2 + 1 + 8 + 9 + 1 + 2}{8} = \frac{40}{8} = 5.0
$$
$$
s^2 = \frac{90}{7} \approx 12.86
$$
$$
s = \sqrt{12.86} \approx 3.58
$$
