Answer:
A. 32, 85, 89, 91, 92, 92
Step-by-step explanation:
A. 32, 85, 89, 91, 92, 92
Mean
[tex]\bar{x}=\dfrac{32+85+89+91+92+92}{6}\\\Rightarrow \bar{x}=80.167[/tex]
Since the number of scores is 6 which is an even number the median will be of the form [tex]\dfrac{x_{n/2}+x_{(n/2)+1}}{2}[/tex]
Median
[tex]\dfrac{89+91}{2}=90[/tex]
Difference of mean and median = [tex]|80.167-90|=9.83[/tex]
B. 72, 78, 79, 80, 82, 82
Mean
[tex]\bar{x}=\dfrac{72+78+79+80+82+82}{6}\\\Rightarrow \bar{x}=78.83[/tex]
Median
[tex]\dfrac{79+80}{2}=79.5[/tex]
Difference of mean and median = [tex]|78.83-79.5|=0.67[/tex]
C. 65, 70, 75, 80, 85, 90
Mean
[tex]\bar{x}=\dfrac{65+70+75+80+85+90}{6}\\\Rightarrow \bar{x}=77.5[/tex]
Median
[tex]\dfrac{75+80}{2}=77.5[/tex]
Difference of mean and median = [tex]|77.5-77.5|=0[/tex]
D. 30, 34, 39, 41, 48, 50
[tex]\bar{x}=\dfrac{30+34+39+41+48+50}{6}\\\Rightarrow \bar{x}=40.33[/tex]
Median
[tex]\dfrac{39+41}{2}=40[/tex]
Difference of mean and median = [tex]|40.33-40|=0.33[/tex]
So, A has the maximum difference of 9.83 between the mean and the median.
