Question

How can I draw a histogram to illustrate this information and How can I calculate the median age of the problem ?

Answer 1

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:

`median=L+((n)/(2)-cf)/(f)c`

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:

`\begin{gathered} L=19.5 \\ n=500 \\ cf=180 \\ f=85 \\ c=10 \end{gathered}`

Plugging these values, we have:

`\begin{gathered} median=19.5+((500)/(2)-180)/(85)(10) \\ median=19.5+(250-180)/(85)(10) \\ median=19.5+(70)/(85)(10) \\ median=27.7353 \end{gathered}`

Therefore, the median is 27.7353