Question 1175995
Let's calculate the mean and standard deviation for the given frequency distribution.

**1. Calculate the Mean (μ)**

* We use the formula: μ = Σ(midpoint * frequency) / Σfrequency
* Σ(midpoint * frequency) = (62 * 2) + (69 * 3) + (76 * 4) + (83 * 1) = 124 + 207 + 304 + 83 = 718
* Σfrequency = 2 + 3 + 4 + 1 = 10
* μ = 718 / 10 = 71.80

**2. Calculate the Standard Deviation (σ)**

* We use the formula: σ = √[Σ(frequency * (midpoint - μ)²) / Σfrequency]
* First, calculate (midpoint - μ)² for each midpoint:
    * (62 - 71.8)² = (-9.8)² = 96.04
    * (69 - 71.8)² = (-2.8)² = 7.84
    * (76 - 71.8)² = (4.2)² = 17.64
    * (83 - 71.8)² = (11.2)² = 125.44
* Next, multiply each result by its corresponding frequency:
    * 96.04 * 2 = 192.08
    * 7.84 * 3 = 23.52
    * 17.64 * 4 = 70.56
    * 125.44 * 1 = 125.44
* Sum these values: 192.08 + 23.52 + 70.56 + 125.44 = 411.6
* Divide by the total frequency: 411.6 / 10 = 41.16
* Take the square root: √41.16 ≈ 6.415606

* Rounding to two decimal places: σ ≈ 6.42

**Answers:**

* Mean (μ) = 71.80
* Standard Deviation (σ) = 6.42