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The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?I. 2II. 4III. 5A) II onlyB) III onlyC) I and II onlyD) II and III onlyE) I, II, and III

Answer :

The median is [tex]7+1/2 = 4[/tex]

4,7,2,8,3,6 automobiles were sold over the course of six days.

I. If there were two automobiles sold on the seventh day, the total number of cars sold over the course of the previous seven days would be  2,2,3,4,6,7,8

Therefore, mean is  

[tex]2+2+3+4+6+7+8/7 = 32/7 =4.57[/tex]

Total number of values =7 (odd) then

the median is [tex]7+1/2 = 4[/tex]

value =4

When four autos are sold on the seventh day, Mean = Median III. If there were five automobiles sold on the seventh day, the total number of cars sold throughout the course of the previous seven days would be 2,3,4,5,6,7,8

Therefore, mean is[tex]2+3+4+5+6+7+8/7=35/7=5[/tex]

Total number of values =7 (odd) then

the median is[tex]7+1/2 = 4[/tex]

value =4 value =5

When there are five autos sold on the seventh day, Mean=Median.

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