Question

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

Answer 1

Hint: According to given in the question we have to check which of the following option will not change for the observation $23,50,27,2x,48,59,72,89,5x,100,120$ when $x$ lies between 15 and 20. So, first of all we have to determine the range for $2x$ and $5x$ which can be determined with the help of as mentioned in the question that $x$ lies between 15 and 20.
So, to obtain the range for $2x$and $5x$we have to substitute the value of range for $x$ lies between 15 and 20 in $2x$ and $5x$
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 $2x$ and $5x$ which can be determined with the help of as mentioned in the question that $x$ lies between 15 and 20.
Step 2: Now, to obtain the range for $2x$ and $5x$ we have to substitute the value of range for $x$lies between 15 and 20 in $2x$ and $5x$. Hence,
As, x lies between 15 and 20 so, $2x$ will lie between 30 and 75.
Step 3: Now, same as the step 2 we have to determine the range for $5x$as mentioned in the question that $x$ lies between 15 and 20. Hence,
As, x lies between 15 and 20 so, $5x$ 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 $2x$ and $5x$ may range between $30,75$ and $40,100$ so, the range of the series will not be affected.
Final solution: Hence, for the observation $23,50,27,2x,48,59,72,89,5x,100,120$ when $x$ 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 $2x$ and $5x$ which can be determined with the help of $x$ 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.