Given Stem-and-Leaf Plot, you know that:
[tex]3|0=\text{ \$}30[/tex]
That means that Stem 3, Leaf 0, means $30.
Knowing the above, you can list all the values given in the Stem-and-Leaf Plot:
[tex]12,25,28,30,32,34,49,56,58,58,59,60,65,65,65,69,75,78[/tex]
(a) By definition, the Median is the middle value of the data set.
In order to find the Median, you can follow these steps:
1. In this case, you already have the values written in ascending order (from the least value to the greatest value).
2. Identify the number of values in the list:
[tex]n=18[/tex]
3. Since there are an even number of values, the Median will be the average of the middle two numbers:
[tex]\begin{gathered} Median=\frac{58+58}{2} \\ \\ Median=58 \end{gathered}[/tex]
(b) By definition, the Mode is the value of the data set that appears most often. In this case, you can identify that this is:
[tex]Mode=65[/tex]
(c) Observe that the cost of the most expensive lamp is $78, and the cost of the least expensive lamp is $12.
Therefore, you need to subtract the cost of the least expensive lamp from the cost of the most expensive lamp, in order to find the Difference in their cost:
[tex]\text{ \$}78-\text{\$}12=\text{\$}66[/tex]
(d) Notice that the costs greater than $20 are:
[tex]25,28,30,32,34,49,56,58,58,59,60,65,65,65,69,75,78[/tex]
And the costs less than $40:
[tex]12,25,28,30,32,34[/tex]
Therefore, you can conclude that the costs greater than $20 but less than $40 are:
[tex]25,28,30,32,34[/tex]
That corresponds to 5 lamps.
(e) Notice that there are 6 lamps that cost less than $40, and there are 12 lamps that cost more than $40. Therefore, the ratio is:
[tex]ratio=\frac{6}{12}=\frac{1}{2}[/tex]
Hence, the answers are:
(a)
[tex]Median=58[/tex]
(b) Yes, there is a Mode:
[tex]Mode=65[/tex]
(c) Difference:
[tex]\text{\$}66[/tex]
(d) Five (5) lamps.
(e) Ratio:
[tex]\frac{1}{2}[/tex]
