Question

Given the sample -6 11, add one more sample value that will neither change the median nor the range. Round to two decimal places as necessary. If this is not possible, indicate "Cannot create sample"

Answer 1

Median is the middle value of the of the sample number given in list , median determined from the range of numbers , first number in arranged in there ascending order and then from sample of numbers middle value is median.

if there is list of even number then in count of term , we will add the two  middle value and then divide by 2

if there is list of odd number then the middle value will median

Range is the difference between the lowest value and highest value in the list of number , it is can be  mean of all the output values of functions ,for example (2,9,5,13,3)

here 13 is highest and 2 is lowest , so range will be (13-2)=11

In this question

sample given = 6,8,11

it is asked what number should be added in sample so that median and range value remain same

so if we add 4 in sample list then range and median will be same .

let prove

sample list 6,8,11,4

To determine median

we will arange the number in ascending order i.e smallest to largest

4,6,8,11

median = 6+8/2

=14/2

median =7

let find Range

6,8,11,4

smallest number 4

largest number 11 , smallest number = 4

range = largest- smallest

=11-4

Range = 7

Hence by adding sample 4 in the given list , it will neither change median nor range .