a) We know that:
[tex]\overline{x}=\frac{\sum_{i=1}^nx_i}{n}.[/tex]
Now, if we change xi by yi and:
[tex]y_i>x_i[/tex]
then:
[tex]\frac{\sum_{i\mathop{=}1}^ny_i}{n}>\frac{\sum_{i\mathop{=}1}^nx_i}{n}.[/tex]
Therefore, if 179 changes to 305, then the mean increases.
The mean of the given values is:
[tex]\frac{179+193+284+299+308+317+436}{7}=288.[/tex]
The mean after change 179 by 305 is:
[tex]\frac{305+193+284+299+308+317+436}{7}=306.[/tex]
Also, notice that:
[tex]306-288=18.[/tex]
b) The median of the given set is:
[tex]299.[/tex]
And the median after change 179 by 305 is:
[tex]305.[/tex]
Therefore the median increases by 6.
Answer:
a) It increases by 18.
b) It increases by 6.
