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Question: Which of the following does not change for the observation \(23,50,27,2x,48,59,72,89,5x,100,120\) wh...

Which of the following does not change for the observation 23,50,27,2x,48,59,72,89,5x,100,12023,50,27,2x,48,59,72,89,5x,100,120 when xx lies between 15 and 20?
A. Arithmetic mean
B. Range
C. Median
D. Quartile deviation

Explanation

Solution

According to given in the question we have to check which of the following option will not change for the observation 23,50,27,2x,48,59,72,89,5x,100,12023,50,27,2x,48,59,72,89,5x,100,120 when xx lies between 15 and 20. So, first of all we have to determine the range for 2x2x and 5x5x which can be determined with the help of as mentioned in the question that xx lies between 15 and 20.
So, to obtain the range for 2x2xand 5x5xwe have to substitute the value of range for xx lies between 15 and 20 in 2x2x and 5x5x
Now, we have to check for the minimum and maximum range or we can say that we have to check for the minimum and maximum value that it is affected or not.

Complete step-by-step solution:
Step 1: First of all we have to determine the range for 2x2x and 5x5x which can be determined with the help of as mentioned in the question that xx lies between 15 and 20.
Step 2: Now, to obtain the range for 2x2x and 5x5x we have to substitute the value of range for xxlies between 15 and 20 in 2x2x and 5x5x. Hence,
As, x lies between 15 and 20 so, 2x2x will lie between 30 and 75.
Step 3: Now, same as the step 2 we have to determine the range for 5x5xas mentioned in the question that xx lies between 15 and 20. Hence,
As, x lies between 15 and 20 so, 5x5x will lie between 40 and 100.
Step 4: Now, we have to check for the minimum and maximum range or we can say that we have to check for the minimum and maximum value that it is affected or not as mentioned in the solution hint. Hence,
As we can see that the numbers 2x2x and 5x5x may range between 30,7530,75 and 40,10040,100 so, the range of the series will not be affected.
Final solution: Hence, for the observation 23,50,27,2x,48,59,72,89,5x,100,12023,50,27,2x,48,59,72,89,5x,100,120 when xx lies between the 15 and 20 range will not be affected.

Therefore option (B) is correct.

Note: To determine the change in minimum and maximum value it is necessary that we have to determine the value of 2x2x and 5x5x which can be determined with the help of xx lies between 15 and 20. Mean is defined as the sum of events divided by the total number of events. The number which appears more often from a set of numbers is called Mode.