Question 1171480
Let's calculate the mean, median, mode, sample variance, and sample standard deviation for the given data.

**1. Mean:**

* **Sum of (x * Freq):** * (1 * 4) + (2 * 2) + (3 * 4) + (6 * 10) = 4 + 4 + 12 + 60 = 80
* **Total Frequency (n):** * 4 + 2 + 4 + 10 = 20
* **Mean (x̄):** * 80 / 20 = 4

**2. Median:**

* Since there are 20 data points, the median is the average of the 10th and 11th values.
* Let's list the values in order:
    * 1 (4 times)
    * 2 (2 times)
    * 3 (4 times)
    * 6 (10 times)
* The 10th and 11th values are both 6.
* Therefore, the median is 6.

**3. Mode:**

* The mode is the value that appears most frequently.
* 6 appears 10 times, which is the highest frequency.
* Therefore, the mode is 6.

**4. Sample Variance (s²):**

* **Calculate (x - x̄)² * Freq:**
    * (1 - 4)² * 4 = (-3)² * 4 = 9 * 4 = 36
    * (2 - 4)² * 2 = (-2)² * 2 = 4 * 2 = 8
    * (3 - 4)² * 4 = (-1)² * 4 = 1 * 4 = 4
    * (6 - 4)² * 10 = (2)² * 10 = 4 * 10 = 40
* **Sum of (x - x̄)² * Freq:**
    * 36 + 8 + 4 + 40 = 88
* **Sample Variance (s²):**
    * 88 / (20 - 1) = 88 / 19 ≈ 4.63

**5. Sample Standard Deviation (s):**

* **Sample Standard Deviation (s):**
    * √s² = √4.63 ≈ 2.15

**Summary:**

* Mean = 4
* Median = 6
* Mode = 6
* Sample Variance ≈ 4.63
* Sample Standard Deviation ≈ 2.15