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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the following frequency distribution table.
| Class interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency | 180 | $f_1$ | 34 | 180 | 136 | $f_2$ | 50 |
If the total frequency is 685 & median is 42.6 then the values of $f_1$ and $f_2$ are
Solution
Median & Frequency Table
Given: Median = 42.6, Total Frequency = 685
Using Median Formula:
\( \text{Median} = L + \left( \frac{N/2 - F}{f} \right) \cdot h \)
- Median Class: 40–50
- Lower boundary \( L = 40 \)
- Frequency \( f = 180 \)
- Class width \( h = 10 \)
- Cumulative freq before median class \( F = 214 + f_1 \)
Substituting values:
\( 42.6 = 40 + \left( \frac{128.5 - f_1}{180} \right) \cdot 10 \Rightarrow f_1 = \boxed{82} \)
Using total frequency:
\( 662 + f_2 = 685 \Rightarrow f_2 = \boxed{23} \)
✅ Final Answer: \( f_1 = 82,\quad f_2 = 23 \)
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