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
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:
[tex]mean=\frac{sum\text{ of observation}}{Total\text{ number of observation}}[/tex]
[tex]\begin{gathered} mean\text{ = }\frac{240+256+307+310+325+333+359+363+378}{9} \\ mean\text{ =}\frac{2871}{9} \\ mean\text{ =319} \end{gathered}[/tex]
if the term 378 changed to 261 then
[tex]\begin{gathered} mean=\text{ }\frac{240+256+307+310+325+333+359+363+261}{9} \\ mean=\text{ }\frac{2754}{9} \\ mean=\text{ 306} \end{gathered}[/tex]
Thus the mean is decreasing.
Decreased value = 319 - 306 = 13
Final answer:
(a) median is decreased by 15
(b) mean is decreased by 13
