Question

For the data below, create a frequency distribution, a cumulative frequencydistribution, a cumulative frequency distribution, and a percentage distribution. Then, calculate and report the mean and mode. Submit a photo of your work.

20, 19, 18, 18, 18, 17, 16, 16, 15, 14, 13, 13, 11

Answer 1

Given data are : 20, 19, 18, 18, 18, 17, 16, 16, 15, 14, 13, 13, 11.

We have to create a frequency distribution, cumulative frequency distribution and a percentage distribution. We know, cumulative frequency of a row is the sum of the frequency of the respective row and the cumulative frequency of the previous row. We know, percentage distribution of a row is (frequency of that row/total frequency)*100.

We will create a table. The table is as follows :

Data Value	Frequency	Cumulative frequency distribution	Percentage distribution
11	1	1	(1/13)*100 = 7.69
13	2	1+2=3	(2/13)*100 = 15.38
14	1	3+1=4	(1/13)*100 = 7.69
15	1	4+1=5	(1/13)*100 = 7.69
16	2	5+2=7	(2/13)*100 = 15.38
17	1	7+1=8	(1/13)*100 = 7.69
18	3	8+3=11	(3/13)*100 = 23.08
19	1	11+1=12	(1/13)*100 = 7.69
20	1	12+1=13	(1/13)*100 = 7.69
Total	13

We have rounded the percentage distribution to two decimal places.

Now, we have to find the mean and mode. We know, Mean = (Sum of all values)/(Total number of values).

Thus, Mean = (11+13+13+14+15+16+16+17+18+18+18+19+20)/13 = 208/13 = 16.

Thus, Mean = 16 .

We know, the value which occurs maximum number of times is called the mode. Here, from our given table, we can see that "18" has occured maximum times. Thus, the mode is 18.

Thus, Mode = 18 .