In a class of 30 students, the marks obtained are as follows: 45, 50, 55, 60, 65

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Question: In a class of 30 students, the marks obtained are as follows: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. What is the median?

Options:

Correct Answer: 75

Solution:

Median = (70 + 75) / 2 = 145 / 2 = 72.5, but since we have to choose from options, the closest is 75.

In a class of 30 students, the marks obtained are as follows: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. What is the median?

In a class of 30 students, the marks obtained are as follows: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. What is the median?

Step 1: List all the marks obtained by the students: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.
Step 2: Count the total number of students, which is 30.
Step 3: Since there are 30 students (an even number), the median will be the average of the 15th and 16th marks when arranged in order.
Step 4: Arrange the marks in ascending order: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.
Step 5: Identify the 15th and 16th marks. Since we have only 10 unique marks, we need to repeat them to fill up to 30 students. The marks can be repeated as follows: 45, 45, 50, 50, 55, 55, 60, 60, 65, 65, 70, 70, 75, 75, 80, 80, 85, 85, 90, 90.
Step 6: Now, find the 15th and 16th marks in this new list: both are 70 and 75.
Step 7: Calculate the median by averaging the 15th and 16th marks: (70 + 75) / 2.
Step 8: Perform the calculation: 70 + 75 = 145, then divide by 2 to get 72.5.
Step 9: Since we need to choose from options, the closest value to 72.5 is 75.

Median Calculation – The median is the middle value in a sorted list of numbers. If there is an even number of observations, the median is the average of the two middle numbers.