Answer:
The new values are as follows:
Mean: 134
Median: 129
Mode: 121
Range=45
Standard Deviation=3.6
Step-by-step explanation:
When a k real number is added to all the elements of the dataset, the new measures of center (mean, median, and mode) are simply found by adding the value k to the previous values. Thus
[tex]Mean_{new}=Mean_{old}+k[/tex]
Here [tex]Mean_{old}[/tex] is 109 and k is 25 thus
[tex]Mean_{new}=Mean_{old}+k\\Mean_{new}=109+25\\Mean_{new}=134[/tex]
Similarly
[tex]Median_{new}=Median_{old}+k[/tex]
Here [tex]Median_{old}[/tex] is 104 and k is 25 thus
[tex]Median_{new}=Median_{old}+k\\Median_{new}=104+25\\Median_{new}=129[/tex]
Also
[tex]Mode_{new}=Mode_{old}+k[/tex]
Here [tex]Mode_{old}[/tex] is 96 and k is 25 thus
[tex]Mode_{new}=Mode_{old}+k\\Mode_{new}=96+25\\Mode_{new}=121[/tex]
When a k real number is added to all the elements of the dataset, the new measures of variation (range and standard deviation) remain the same thus.
[tex]Range_{new}=Range_{old}\\Range_{new}=45[/tex]
Similarly
[tex]Standard\ Deviation_{new}=Standard\ Deviation_{old}\\Standard\ Deviation_{new}=3.6[/tex]
So the new values of mean, median, mode, range, and standard deviation are 134, 129, 121, 45, and 3.6 respectively.
