For the following distribution:
| Class | 0–5 | 5–10 | 10–15 | 15–20 | 20–25 |
|---|---|---|---|---|---|
| Frequency | 10 | 15 | 12 | 20 | 9 |
the sum of lower limits of the median class and modal class is
15
25
30
35
Step 1: Find the total number of observations (N).
Add all frequencies: \(10 + 15 + 12 + 20 + 9 = 66\).
So, \(N = 66\).
Step 2: Find the median class.
We need \(N/2 = 66/2 = 33\).
Now make the cumulative frequencies:
We check where the 33rd observation lies. It lies in the class 10–15 because up to 25 it is not reached, but at 37 it crosses 33.
So, the median class is 10–15 and its lower limit = 10.
Step 3: Find the modal class.
The class with the highest frequency is the modal class.
Here the highest frequency is 20, in the class 15–20.
So, the modal class is 15–20 and its lower limit = 15.
Step 4: Add the two lower limits.
Median class lower limit = 10
Modal class lower limit = 15
Sum = 10 + 15 = 25
Final Answer: Option B (25)