Question

The numbers of students in the 7 schools are given below. ( Note that these are already ordered from least to greatest.)

Answer 1

a) We know that:

`\overline{x}=(\sum_(i=1)^nx_i)/(n).`

Now, if we change xi by yi and:

`y_i>x_i`

then:

`\frac{\sum_{i\mathop{=}1}^ny_i}{n}>\frac{\sum_{i\mathop{=}1}^nx_i}{n}.`

Therefore, if 179 changes to 305, then the mean increases.

The mean of the given values is:

`(179+193+284+299+308+317+436)/(7)=288.`

The mean after change 179 by 305 is:

`(305+193+284+299+308+317+436)/(7)=306.`

Also, notice that:

`306-288=18.`

b) The median of the given set is:

`299.`

And the median after change 179 by 305 is:

`305.`

Therefore the median increases by 6.

Answer:

a) It increases by 18.

b) It increases by 6.