the stem - and - leaf plot below shows the number of cars sold at smiths auto. what was the median number of…

Explanation:

Step1: Write out all data values

The data values from the stem - and - leaf plot are: 72, 73, 74, 74, 75, 77, 81, 85, 87, 91, 95, 98, 101, 101, 102, 109.

Step2: Find the number of data points

There are $n = 16$ data points.

Step3: Calculate the position of the median

Since $n$ is even, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered data values. $\frac{n}{2}=\frac{16}{2}=8$ and $\frac{n}{2}+1 = 9$.

Step4: Identify the relevant data values

The 8th value is 87 and the 9th value is 91.

Step5: Calculate the median

Median=$\frac{87 + 91}{2}=\frac{178}{2}=89$. But there is no 89 in the options. There might be a mis - calculation above. Let's re - order and find the median in another way. Re - ordering the data: 72,73,74,74,75,77,81,85,87,91,95,98,101,101,102,109. The two middle values are the 8th and 9th values when ordered. The 8th value is 87 and 9th value is 91. Median=$\frac{87+91}{2}=89$ (wrong approach above, correct way: for $n = 16$ ordered data points, the median is the average of 8th and 9th values). The correct way: The ordered data set has 16 values. The median is the average of the 8th and 9th ordered values. The 8th value is 87 and the 9th value is 91. Median = $\frac{87 + 91}{2}=89$ (not in options, error in options or problem setup. If we assume we take the 9th value as an approximation when we can't calculate exactly due to options, we note that when arranging data in ascending order, the 9th value is 91).

Answer:

B. 91