Question

The number of cars sold at 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. $2$
II. $4$
III. $5$

• A. II only
• B. III only
• C. I and II only
• D. I and III onlu
• E. I, II and III

Answer 1

The correct option is B III only

Mean is the sum of the data values divided by the total number of data values.

Median is the middle value of the data values after arranging the data values in the ascending or descending order.

If $n$ is odd, then the median is $(\frac{n+1}{2}{)}^{th}$ value.

If $n$ is even, then the median is ${\frac{(\frac{n}{2}{)}^{th}+(\frac{n}{2}+1)}{2}}^{th}$ value.

Number of cars sold on six days is $4,7,2,8,3,6$

$I.$ If the number of cars sold on the seventh day is $2$

Total cars sold on seven days after arranging in ascending order are $2,2,3,4,6,7,8$

Therefore, mean is $\frac{2+2+3+4+6+7+8}{7}=\frac{32}{7}=4.57$

Total number of values $=7$ (odd) then

the median is $(\frac{7+1}{2}{)}^{th}$ value = $4^{th}$ value =$4$

If the number of cars sold on the seventh day is $2$ then $Mean\ne Median$

$II.$ If the number of cars sold on the seventh day is $4$

Total cars sold on seven days after arranging in ascending order are $2,3,4,4,6,7,8$

Therefore, mean is $\frac{2+3+4+4+6+7+8}{7}=\frac{34}{7}=4.85$

Total number of values $=7$ (odd) then

the median is $(\frac{7+1}{2}{)}^{th}$ value = $4^{th}$ value =$4$

If the number of cars sold on the seventh day is $4$ then $Mean\ne Median$

$III.$ If the number of cars sold on the seventh day is $5$

Total cars sold on seven days after arranging in ascending order are $2,3,4,5,6,7,8$

Therefore, mean is $\frac{2+3+4+5+6+7+8}{7}=\frac{35}{7}=5$

Total number of values $=7$ (odd) then

the median is $(\frac{7+1}{2}{)}^{th}$ value = $4^{th}$ value =$5$

If the number of cars sold on the seventh day is $5$ then $Mean=Median$