Among 16 observations, if the least observation is eliminated the average of the remaining observations is 60. if the greatest observation is eliminated the average of the remaining observations is 54. For the 16 observations, find the difference between the maximum possible average and the minimum possible average.?

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Among 16 observations, if the least observation is eliminated the aver...

**Given Information:**

- There are 16 observations.
- When the least observation is eliminated, the average of the remaining observations is 60.
- When the greatest observation is eliminated, the average of the remaining observations is 54.

**Let's solve the problem step by step:**

**Step 1: Find the sum of the observations**
- We know that the average is the sum of all observations divided by the number of observations.
- Let's assume the sum of all observations is 'S'.

**Step 2: Find the sum of the remaining observations when the least observation is eliminated**
- We have 16 observations, so when the least observation is eliminated, we have 15 observations.
- The average of the remaining observations is given as 60.
- Therefore, the sum of the remaining observations is 15 * 60 = 900.

**Step 3: Find the sum of the remaining observations when the greatest observation is eliminated**
- Similar to the previous step, we have 15 observations when the greatest observation is eliminated.
- The average of the remaining observations is given as 54.
- Therefore, the sum of the remaining observations is 15 * 54 = 810.

**Step 4: Find the least and greatest observations**
- From the given information, we can deduce that the least observation is less than or equal to 54, and the greatest observation is greater than or equal to 60.

**Step 5: Find the maximum possible average**
- To find the maximum possible average, we need to maximize the sum of the observations.
- Since the greatest observation is eliminated, we want the greatest observation to be as large as possible.
- From Step 4, we know that the greatest observation is greater than or equal to 60.
- Therefore, let's assume the greatest observation is 60.

**Step 6: Find the minimum possible average**
- To find the minimum possible average, we need to minimize the sum of the observations.
- Since the least observation is eliminated, we want the least observation to be as small as possible.
- From Step 4, we know that the least observation is less than or equal to 54.
- Therefore, let's assume the least observation is 54.

**Step 7: Find the difference between the maximum and minimum possible averages**
- The maximum possible average is the sum of the observations when the greatest observation is 60 divided by 16.
- The minimum possible average is the sum of the observations when the least observation is 54 divided by 16.
- The difference between the maximum and minimum possible averages is the maximum possible average minus the minimum possible average.

**Step 8: Calculate the difference between the maximum and minimum possible averages**
- The maximum possible average = (Sum of observations when greatest observation is 60) / 16
- The minimum possible average = (Sum of observations when least observation is 54) / 16
- Difference = Maximum possible average - Minimum possible average

**Step 9: Simplify the equation**
- The sum of the observations when the greatest observation is 60 is 900 (from Step 3).
- The sum of the observations when the least observation is 54 is 810 (from Step 3).
- The maximum possible average = 900 / 16 = 56.25
- The minimum possible average = 810 / 16 = 50.625
-

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Among 16 observations, if the least observation is eliminated the average of the remaining observations is 60. if the greatest observation is eliminated the average of the remaining observations is 54. For the 16 observations, find the difference between the maximum possible average and the minimum possible average.? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Among 16 observations, if the least observation is eliminated the average of the remaining observations is 60. if the greatest observation is eliminated the average of the remaining observations is 54. For the 16 observations, find the difference between the maximum possible average and the minimum possible average.? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Among 16 observations, if the least observation is eliminated the average of the remaining observations is 60. if the greatest observation is eliminated the average of the remaining observations is 54. For the 16 observations, find the difference between the maximum possible average and the minimum possible average.?.

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