Question

How do I draw How do I draw a cumulative frequency table ? and a cumulative curve? How can I use the cumulative frequency curve to estimate the median time how do I know many people took less than 75 minutes ? How many people took more than 90 minutes How do I know what was the average time taken to complete the walkathon?

Answer 1

In order to create a cumulative frequency table, add another column to the table and name it cumulative frequency.

Then, start writing the first frequency on the first row, then on the next row, add the second frequency, then on the next row, add the third frequency, until the last frequency. See the table below:

The last row should show the sum of the frequency which in this case is 100.

In order to draw a cumulative frequency curve, note that the intervals "x" in minutes will be our x-axis and the cumulative frequency will be our y-axis.

b. The median time would be the centermost data in the graph. Since there are 100 people, the centermost data would be found between 50th and 51st. So, looking at the curve, the median is found approximately between 71 - 80 minutes.

c. Based on the cumulative frequency, there were approximately 59 people who took less than 75 minutes.

d. Based on the cumulative frequency, there were 20 people who took more than 90 mins.

e. To determine the average, we need to add another column in the table and we will name this the class mark. Class Mark is the center between the intervals. For example, interval 41 - 50 has a center of 45.5.

Then, let's multiply each frequency by the class mark and put the answer in another column. For example, 2 x 45.5 = 91.

Add the results in the last column and divide them by 100 since total frequency = 100.

$\begin{gathered} 91+610.5+1179+2114=3994.5 \\ 1795.5+1146+527.5+346.5=3815.5 \\ 3994.5+3815.5=7810 \end{gathered}$

The total is 7,810.

$7,810\div100=78.1$

Therefore, the average time taken to complete the walkathon is 78.1 minutes.