1. **State the problem:** We need to find the sample standard deviation of the mileage (MPG) for the sample of convertibles: 25, 25, 24, 21, 21, 21.
2. **Recall the formula for sample standard deviation:**
$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$
where $n$ is the sample size, $x_i$ are the data points, and $\bar{x}$ is the sample mean.
3. **Calculate the sample mean $\bar{x}$:**
$$\bar{x} = \frac{25 + 25 + 24 + 21 + 21 + 21}{6} = \frac{137}{6} \approx 22.8333$$
4. **Calculate each squared deviation $(x_i - \bar{x})^2$:**
- $(25 - 22.8333)^2 = (2.1667)^2 \approx 4.6944$
- $(25 - 22.8333)^2 = 4.6944$
- $(24 - 22.8333)^2 = (1.1667)^2 \approx 1.3611$
- $(21 - 22.8333)^2 = (-1.8333)^2 \approx 3.3611$
- $(21 - 22.8333)^2 = 3.3611$
- $(21 - 22.8333)^2 = 3.3611$
5. **Sum the squared deviations:**
$$4.6944 + 4.6944 + 1.3611 + 3.3611 + 3.3611 + 3.3611 = 20.8332$$
6. **Divide by $n-1 = 5$:**
$$\frac{20.8332}{5} = 4.16664$$
7. **Take the square root to find $s$:**
$$s = \sqrt{4.16664} \approx 2.0412$$
8. **Round to at least one decimal place:**
$$s \approx 2.0$$
**Final answer:** The sample standard deviation of the mileage for the convertibles is approximately **2.0**.
Sample Std Dev 3Cc253
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