Question
Download Solution PDFIf x and y are upper limit of median class and lower limit of modal class respectively in the following distribution, then what is the value of (2x + y) ?
| Marks | Below 10 | Below 20 | Below 30 | Below 40 | Below 50 | Below 60 |
| No. of students | 3 | 22 | 35 | 47 | 55 | 80 |
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
For median class: Calculate N/2. The class whose cumulative frequency is greater than and nearest to N/2 is the median class. The upper limit of this class is x.
For modal class: Convert the cumulative frequency distribution to a simple frequency distribution. The class with the highest frequency is the modal class. The lower limit of this class is y.
Calculation:
First, create a frequency distribution table from the given cumulative frequency distribution:
| Marks (Class Interval) | No. of students (f) | Cumulative Frequency (cf) |
| 0-10 | 3 | 3 |
| 10-20 | 22 - 3 = 19 | 22 |
| 20-30 | 35 - 22 = 13 | 35 |
| 30-40 | 47 - 35 = 12 | 47 |
| 40-50 | 55 - 47 = 8 | 55 |
| 50-60 | 80 - 55 = 25 | 80 |
Total number of students (N) = 80
Median Class = N/2 = 80/2 = 40
The cumulative frequency just greater than 40 is 47, which corresponds to the class interval 30-40.
So, the median class is 30-40.
The upper limit of the median class (x) = 40.
Modal Class: The highest frequency in the frequency column is 25, which corresponds to the class interval 50-60.
So, the modal class is 50-60.
The lower limit of the modal class (y) = 50.
Calculating (2x + y):
2x + y = 2 × 40 + 50
⇒ 2x + y = 80 + 50
⇒ 2x + y = 130
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