Answer :
Answer:
14
Step-by-step explanation:
To find the median of a grouped frequency distribution, we first need to calculate the cumulative frequencies. Then, we locate the median class, which is the class where the cumulative frequency exceeds N/2 (where N is the total frequency). Finally, we use the median formula to find the exact median within the median class.
Here's how you can do it:
1. Calculate the cumulative frequencies:
Class interval: 0-5, 5-10, 10-15, 15-20, 20-25
Frequency: 3, 6, 5, 7, 5
Cumulative frequencies:
0-5: 3
5-10: 3 + 6 = 9
10-15: 9 + 5 = 14
15-20: 14 + 7 = 21
20-25: 21 + 5 = 26
2. Find the median class:
The median class is the class where the cumulative frequency exceeds N/2. Here, N = 26/2 = 13. So, the median class is the class with a cumulative frequency greater than 13. That is the 10-15 class.
3. Use the median formula:
Median = L + [(N/2 - F) / f] * w
Where:
L = Lower boundary of the median class (10 in this case)
N = Total frequency (26)
F = Cumulative frequency of the class before the median class (9)
f = Frequency of the median class (5)
w = Width of the class interval (5 - 10 = 5)
Median = 10 + [(13 - 9) / 5] * 5
= 10 + (4/5) * 5
= 10 + 4
= 14
So, the median of the given distribution is 14.
