Question 1176041
**1. Calculate the Midpoints**

* Find the midpoint of each class interval:
    * 46-50: (46 + 50) / 2 = 48
    * 41-45: (41 + 45) / 2 = 43
    * 36-40: (36 + 40) / 2 = 38
    * 31-35: (31 + 35) / 2 = 33
    * 26-30: (26 + 30) / 2 = 28

**2. Mean**

* Use the formula:
    * Mean (x̄) = Σ(midpoint * frequency) / Σfrequency
* x̄ = [(48 * 2) + (43 * 9) + (38 * 10) + (33 * 14) + (28 * 10)] / (2 + 9 + 10 + 14 + 10)
* x̄ = (96 + 387 + 380 + 462 + 280) / 45
* x̄ = 1605 / 45
* x̄ ≈ 35.67

**3. Median**

1.  **Find the Cumulative Frequencies:**
    * 46-50: 2
    * 41-45: 2 + 9 = 11
    * 36-40: 11 + 10 = 21
    * 31-35: 21 + 14 = 35
    * 26-30: 35 + 10 = 45

2.  **Identify the Median Class:**
    * The total number of scores (N) is 45.
    * The median class is the class where the cumulative frequency is greater than or equal to N/2 (which is 22.5 in this case).
    * The median class is 31-35.

3.  **Calculate the Median:**
    * Use the formula:
        * Median = L + [(N/2 - cf) / f] * w
    * Where:
        * L = Lower boundary of the median class (30.5)
        * N = Total number of scores (45)
        * cf = Cumulative frequency of the class before the median class (21)
        * f = Frequency of the median class (14)
        * w = Class width (5)
    * Median = 30.5 + [(22.5 - 21) / 14] * 5
    * Median = 30.5 + (1.5 / 14) * 5
    * Median ≈ 31.04

**4. Mode**

* The modal class is the class with the highest frequency.
* In this case, the modal class is 31-35.

**Summary**

* Mean: 35.67
* Median: 31.04
* Mode: 31-35