High School

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The median of the following data is:

Marks:
- 0-10
- 10-20
- 20-30
- 30-40
- 40-50
- 50-60
- 60-70

Number of students:
- 15
- 25
- 52
- 56
- 78
- 80
- 70

Options:
A) 30-40
B) 40-50
C) 50-60
D) 60-70

Answer :

Final answer:

The median of the grouped data falls in the 40-50 interval, determined by calculating the total number of students, finding the median position, and identifying the cumulative frequency up to that position. Option B is the answer.

Explanation:

The subject question relates to finding the median of a grouped data set which involves the distribution of marks among a number of students. To find the median interval in a grouped data set, we first need to determine the total number of students, which we do by summing the number of students in each interval. Once we have the total, we can calculate the median position using the formula (n + 1) / 2, where n is the total number of observations. We then find the cumulative frequency up to the median position to identify the class interval containing the median.

For this dataset:
Total number of students = 15 + 25 + 52 + 56 + 78 + 80 + 70 = 376
Median position = (376 + 1) / 2 = 188.5
The cumulative frequency just before the median position is in the 30-40 interval (15 + 25 + 52 = 92). Adding the next group's frequency (56) to 92 exceeds 188.5 (148), so the median falls in the 40-50 interval.

Thus, the correct option is B) 40-50.

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