Answer:
(a) 43
(b) 40
(c)
It is not possible to add a number to the data set that would decrease the range.
For a number between minimum and maximum, the range will not change.
If a number is added above the maximum, the range will increase.
If a number is added above the minimum, the range will increase.
Step-by-step explanation:
Range of a set of data is the difference between the maximum value and the minimum value.
From the given data in the figure,
The maximum value is = 68
The minimum value is = 42
Therefore, the range is given as:
Range = Maximum value - Minimum value
Range = 68 - 42 = 26
(a)
The range only depends on the maximum and minimum value of the data. So, a number greater than or equal to minimum value and less than or equal to maximum value will not change range.
Therefore, if the added number is 'x' that don't change the range, then
[tex]42\leq x\leq68[/tex]
So, one value of 'x' can be [tex] x = 43[/tex]
Range = Maximum value - Minimum value = 68 - 42 = 26
(b)
If 'y' is a number that changes the range, then
[tex]y<42\ or\ y>68[/tex]
As this will change the minimum or maximum value and hence the range is changed.
Let [tex]y=40[/tex]
Range = Maximum value - Minimum value = 68 - 40 = 28
(c)
No, it is not possible to add a number that would decrease the range.
If we add a number greater than the original maximum value or less than the original minimum value, then range will only increase.
Let the number added be 70. Now, maximum value = 70 and minimum value = 42.
Range = 70 - 42 = 28 > 26
Let the number added be 30. Now, maximum value = 68 and minimum value = 30.
Range = 68 - 30 = 38 > 26
It is not possible to add a number to the data set that would decrease the range.
From (a), we see that, for a number between minimum and maximum, the range will not change.
From (c), we see that, if a number is added above the maximum, the range will increase.
From (c), we see that, if a number is added above the minimum, the range will increase.
