Question 1172923
**1. Median**

* **Find the cumulative frequency:**
    * 10-19: 5
    * 20-29: 5 + 25 = 30
    * 30-39: 30 + 40 = 70
    * 40-49: 70 + 20 = 90
    * 50-59: 90 + 10 = 100

* **Identify the median class:**
    * The total number of students is 100.
    * The median is the value that divides the data into two equal halves, so we need the 50th value.
    * The cumulative frequency that includes the 50th value is 70, which corresponds to the 30-39 class.

* **Calculate the median:**
    * Median = L + [(N/2 - CF) / f] * h
        * L = lower limit of the median class = 30
        * N = total number of students = 100
        * CF = cumulative frequency of the class before the median class = 30
        * f = frequency of the median class = 40
        * h = class width = 10
    * Median = 30 + [(100/2 - 30) / 40] * 10
    * Median = 30 + (20/40) * 10
    * Median = 30 + 5
    * **Median = 35**

**2. Mode**

* **Identify the modal class:**
    * The modal class is the class with the highest frequency.
    * In this case, the modal class is 30-39 with a frequency of 40.

* **Calculate the mode:**
    * Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] * h
        * L = lower limit of the modal class = 30
        * f1 = frequency of the modal class = 40
        * f0 = frequency of the class before the modal class = 25
        * f2 = frequency of the class after the modal class = 20
        * h = class width = 10
    * Mode = 30 + [(40 - 25) / (2 * 40 - 25 - 20)] * 10
    * Mode = 30 + (15 / 35) * 10
    * Mode = 30 + 4.29
    * **Mode = 34.29**

**Therefore:**

* **Median = 35**
* **Mode = 34.29**