Median of a group of 20 distinct numbers was
found to be 55. If largest 8 numbers are
increased by 10, then median of the new group,
is
Answers
Answered by
21
Hey there!
Median of n observations , if n is even = A. M of( n/2 , n/2+1)th terms.
Now, For the Given data.
Number of observations = 20 .
⇒ Now, 20 is odd.
So, Median = A. M of ( 10 , 11 th terms).
According to the question, Median = 55
We observe that The decrement in first 9 terms , or Increment in last 9 terms won't affect Median.
In other words, Decrement in the 9 smallest and increment in 9 largest terms won't affect the median.
According to the question, Largest 8 terms are increased by 10 . As we already discussed .This doesn't affect median .
So, Median of the new group = 55 .[ Remains Unchanged ]
The Median of New Group is 55 .
Median of n observations , if n is even = A. M of( n/2 , n/2+1)th terms.
Now, For the Given data.
Number of observations = 20 .
⇒ Now, 20 is odd.
So, Median = A. M of ( 10 , 11 th terms).
According to the question, Median = 55
We observe that The decrement in first 9 terms , or Increment in last 9 terms won't affect Median.
In other words, Decrement in the 9 smallest and increment in 9 largest terms won't affect the median.
According to the question, Largest 8 terms are increased by 10 . As we already discussed .This doesn't affect median .
So, Median of the new group = 55 .[ Remains Unchanged ]
Answered by
14
Hi.
Here is your answer---
__________________
Answer--- The Medium will not change.
Explanation-- While Calculating the Medium, we first arrange the Number is an ascending or an descending order. By doing so, the Median can be calculated Perfectly.
We know,If the number of terms is odd, then there will be one median term, when the number of terms in the group is even, then there will be two middle term.
In the above given case,the number of terms is 20, which is a even number.
Thus, Median = [(n/2)th term + {(n /2) + 1}th term] ÷ 2
= [(20/2)th term + {(20/2) + 1}th term] ÷ 2
= [10th term + (10 + 1)th term] ÷ 2
= [10th term + 11th term] ÷ 2.
From this we can observe that, the value of median is depend upon only 11th and 12th term. So, if there will either increment or decrements is first or last 9 th term, there will no change in the Value of the Median.
As per as the Question, if the first 8 term increased by 10, then also there will be no change in the Value of the Median, as it does not effect the 10th and the 11th term.
Thus, the median remains the Same.The Value of the Medium will be fixed at 55, either there will increment or decrements in the first or the last 9 terms.
___________________
Hope it helps.
Have a nice day.
Here is your answer---
__________________
Answer--- The Medium will not change.
Explanation-- While Calculating the Medium, we first arrange the Number is an ascending or an descending order. By doing so, the Median can be calculated Perfectly.
We know,If the number of terms is odd, then there will be one median term, when the number of terms in the group is even, then there will be two middle term.
In the above given case,the number of terms is 20, which is a even number.
Thus, Median = [(n/2)th term + {(n /2) + 1}th term] ÷ 2
= [(20/2)th term + {(20/2) + 1}th term] ÷ 2
= [10th term + (10 + 1)th term] ÷ 2
= [10th term + 11th term] ÷ 2.
From this we can observe that, the value of median is depend upon only 11th and 12th term. So, if there will either increment or decrements is first or last 9 th term, there will no change in the Value of the Median.
As per as the Question, if the first 8 term increased by 10, then also there will be no change in the Value of the Median, as it does not effect the 10th and the 11th term.
Thus, the median remains the Same.The Value of the Medium will be fixed at 55, either there will increment or decrements in the first or the last 9 terms.
___________________
Hope it helps.
Have a nice day.
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