Question 1179844
Here's how to calculate the sample mean and sample standard deviation for the given frequency distribution:

**A. Sample Mean (x̄):**

1.  **Calculate the sum of (x * frequency):**
    * (1 * 3) + (2 * 7) + (4 * 10) + (6 * 8) + (7 * 4) = 3 + 14 + 40 + 48 + 28 = 133

2.  **Calculate the total frequency (n):**
    * 3 + 7 + 10 + 8 + 4 = 32

3.  **Calculate the sample mean:**
    * x̄ = (sum of (x * frequency)) / n
    * x̄ = 133 / 32 ≈ 4.16

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

1.  **Calculate (x - x̄)² for each x:**
    * (1 - 4.16)² ≈ 9.99
    * (2 - 4.16)² ≈ 4.67
    * (4 - 4.16)² ≈ 0.03
    * (6 - 4.16)² ≈ 3.39
    * (7 - 4.16)² ≈ 8.07

2.  **Multiply each (x - x̄)² by its frequency:**
    * 9.99 * 3 ≈ 29.97
    * 4.67 * 7 ≈ 32.69
    * 0.03 * 10 ≈ 0.3
    * 3.39 * 8 ≈ 27.12
    * 8.07 * 4 ≈ 32.28

3.  **Calculate the sum of the results from step 2:**
    * 29.97 + 32.69 + 0.3 + 27.12 + 32.28 = 122.36

4.  **Divide by (n - 1):**
    * 122.36 / (32 - 1) = 122.36 / 31 ≈ 3.947

5.  **Take the square root:**
    * s = √3.947 ≈ 1.99

**Answers:**

A. Sample mean: 4.16
B. Sample standard deviation: 1.99