Answer
* **Variance** $s^2 \approx 33.16$
* **Standard Deviation** $s \approx 5.76$
Work Step by Step
We’re given:
* $N = 21$
* $\sum X = 304$
* $\sum X^2 = 5064$
Because the researcher is trying to **estimate the standard deviation for the entire population**, but only has a **sample**, we use the **sample variance formula**:
---
### **Sample Variance (s²) Formula**
$$
s^2 = \frac{\sum X^2 - \frac{(\sum X)^2}{N}}{N - 1}
$$
---
### **Plug in values:**
$$
s^2 = \frac{5064 - \frac{304^2}{21}}{20}
$$
$$
\frac{304^2}{21} = \frac{92416}{21} \approx 4400.76
$$
$$
s^2 = \frac{5064 - 4400.76}{20} = \frac{663.24}{20} \approx 33.16
$$
---
### **Sample Standard Deviation (s)**
$$
s = \sqrt{33.16} \approx 5.76
$$
