The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations is increased by 2, then the median of the new set :a)is increased by 2b)is decreased by 2c)is two time the original mediand)remains the same as that of original setCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given Information:

Set of 9 distinct observations

Median of the set is 20.5

Explanation:

To understand why the median of the new set remains the same as that of the original set, we need to understand what the median represents and how it is affected by changes in the data.

Median:

The median is the middle value of a set of data when it is arranged in ascending or descending order. It divides the data into two halves, with 50% of the values being less than or equal to the median, and the other 50% being greater than or equal to the median.

Effect of Increasing Largest 4 Observations by 2:

When the largest 4 observations are increased by 2, it does not change the relative order of the observations. The new set still has the same values, just increased by 2. Therefore, the position of the median in the new set remains the same.

Proof:

Let's consider an example to illustrate this:

Original set: 10, 15, 18, 20, 21, 23, 25, 30, 40
Arranged set: 10, 15, 18, 20, 21, 23, 25, 30, 40
Median (original set) = 20.5

After increasing largest 4 observations by 2:
New set: 10, 15, 18, 20, 21, 23, 25, 32, 42
Arranged set: 10, 15, 18, 20, 21, 23, 25, 32, 42
Median (new set) = 20.5

As you can see, the median of the new set is still 20.5, which is the same as the median of the original set. This example demonstrates that increasing the largest 4 observations by 2 does not affect the median.

Conclusion:

The median of the new set remains the same as that of the original set, regardless of the specific values in the set. This is because increasing the largest 4 observations by 2 does not change the relative order of the observations, and hence does not affect the position of the median.

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