Median Mode Sum 97312C
1. **Problem:** Find the sum of the lower limits of the median class and mode class from the given frequency distribution.
Class intervals: 0-5, 5-10, 10-15, 15-20, 20-25
Frequencies: 10, 15, 12, 20, 9
2. **Median class:** The class where the cumulative frequency reaches or exceeds half the total frequency.
Total frequency $=10+15+12+20+9=66$
Half total frequency $=\frac{66}{2}=33$
Cumulative frequencies:
- 0-5: 10
- 5-10: 10+15=25
- 10-15: 25+12=37
- 15-20: 37+20=57
- 20-25: 57+9=66
Median class is 10-15 because cumulative frequency crosses 33 here.
3. **Mode class:** The class with the highest frequency.
Frequencies: 10, 15, 12, 20, 9
Highest frequency is 20 in class 15-20.
4. **Sum of lower limits:**
Lower limit of median class = 10
Lower limit of mode class = 15
Sum $=10+15=25$
**Answer:** (b) 25
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Since the instruction is to solve only the first question, we stop here.