Answer:
the difference between the upper limit of the modal class and the lower limit of the median class is 10.
Step-by-step explanation:
To find the difference between the upper limit of the modal class and the lower limit of the median class, we first need to identify the modal class and the median class.
1. **Modal Class:**
The modal class is the class interval with the highest frequency. In this case, the class interval with the highest frequency is 10-20.
2. **Median Class:**
The median class is the class interval that contains the median of the data. To find the median class, we need to calculate the cumulative frequency and locate the class interval containing the median.
Given the data:
Marks | Marks if Students
--------|-------------------
0-10 | 2
10-30 | 5 + 17 + 10 = 32
10-20 | 17
20-30 | 10
30-40 | 16
40-50 | (Assuming) 0
The cumulative frequencies are:
- For 0-10: 2
- For 10-30: 2 + 32 = 34
- For 10-20: 2 + 17 = 19
- For 20-30: 2 + 17 + 10 = 29
- For 30-40: 2 + 17 + 10 + 16 = 45
- For 40-50: 2 + 17 + 10 + 16 + 0 = 45
Since the total number of students is 2 + 5 + 17 + 10 + 16 = 50, the median class is the one where the cumulative frequency crosses halfway through the total, which is 25 students.
Looking at the cumulative frequency, we see that the 25th student falls within the 10-20 class interval, making it the median class.
Now, the difference between the upper limit of the modal class (20) and the lower limit of the median class (10) is:
Difference = Upper Limit of Modal Class - Lower Limit of Median Class
= 20 - 10
= 10
