Question

The numbers of students in the 9 schools in a district are given below. (NOTE THAT THESE ARE ALL ALREADY IN ORDER FROM LEST TO GREATEST)

Answer 1

Given:

The data is:

240,256, 307, 310, 325, 333, 359, 363, 378

Required:

If the number 378 changes to 261 then

(a) What happens to the median

(b) What happens to the mean

Step-by-step explanation:

(a)The number of terms = 9

Median = 5th term

Median = 325

if the term 378 changed to 261 then the data will be:

240,256, 261 307, 310, 325, 333, 359, 363

Median = 310

Thus the median is decreasing.

Decreased value = 325 - 310 = 15

(b) Mean is given by the formula:

`mean=\frac{sum\text{ of observation}}{Total\text{ number of observation}}`

`\begin{gathered} mean\text{ = }(240+256+307+310+325+333+359+363+378)/(9) \\ mean\text{ =}(2871)/(9) \\ mean\text{ =319} \end{gathered}`

if the term 378 changed to 261 then

`\begin{gathered} mean=\text{ }(240+256+307+310+325+333+359+363+261)/(9) \\ mean=\text{ }(2754)/(9) \\ mean=\text{ 306} \end{gathered}`

Thus the mean is decreasing.

Decreased value = 319 - 306 = 13

Final answer:

(a) median is decreased by 15

(b) mean is decreased by 13