Question 1172923: Compute the median and mode of the following distribution
Marks 10-19 20-29 30-39 40-49 50-59
No. of students 5 25 40 20 10
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **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**
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