To draw a histogram we first need to draw the bins, since we have eight classes, we will need to draw eight equal lengths. After we do this, we draw rectangles with a height representing the frequency of each class. Then the histogram of this table is:
To find the median of grouped data we have to use the formula:
[tex]median=L+\frac{\frac{n}{2}-cf}{f}c[/tex]
where:
• L is the lower boundary point of median class
,
• n is the total frequency
,
• cf is the cumulative frequency of the class preceding the median class
,
• f is the frequency of the median class
,
• c is the class length of median class
Then we need the cumulative frequency of each class, this is shown in the following table:
To find the median class we divide the total number of observations by two, then we get 250. Now, we look at the class where this cumulative frequency will lie; from the previous table we notice that this happens in the 20-29 class.
Since we need the real limits we will use the median class as 19.5-29.5. Once we know this, we have that:
[tex]\begin{gathered} L=19.5 \\ n=500 \\ cf=180 \\ f=85 \\ c=10 \end{gathered}[/tex]
Plugging these values, we have:
[tex]\begin{gathered} median=19.5+\frac{\frac{500}{2}-180}{85}(10) \\ median=19.5+\frac{250-180}{85}(10) \\ median=19.5+\frac{70}{85}(10) \\ median=27.7353 \end{gathered}[/tex]
Therefore, the median is 27.7353
