Answer:
D. I and III only
Step-by-step explanation:
Number of first fie defects are given as 9,7,10,4 and 6.
First we have to arrange the above data in ascending order which is 4,6,7,9,10
So the mean of above data would be [tex]\frac{3+4+6+7+9+10}{6}[/tex] = 6.5
and Median of the above data would be = [tex]\frac{3^{rd} obs + 4^{th} obs}{2}[/tex] = [tex]\frac{6+7}{2}[/tex] = 6.5
Hence mean and median number of defects are same if the sixth car has 3 defects.
So the mean of above data would be [tex]\frac{4+6+7+9+10+12}{6}[/tex] = 8
and Median of the above data would be = [tex]\frac{3^{rd} obs + 4^{th} obs}{2}[/tex] = [tex]\frac{7+9}{2}[/tex] = 8
Hence mean and median number of defects are same if the sixth car has 12 defects.
So the mean of above data would be [tex]\frac{4+6+7+7+9+10}{6}[/tex] = 7.167
and Median of the above data would be = [tex]\frac{3^{rd} obs + 4^{th} obs}{2}[/tex] = 7
Hence mean and median number of defects are not same if the sixth car has 7 defects.
Therefore option D is correct.