In a bar graph each bar represents a specific category.
B
To create a circle graph, we need to have percentages.
C
Which graph should be used in case of frequencies?
D
How can we describe a distribution where frequencies of all categories are similar to each other?
A
B
C
See solution.
D
See solution.
Practice makes perfect
We are told that mathematicians, with the help of computers, analyzed the frequency of each of the numbers 0 through 9 in the first 100 000 digits of π. Let's take a look at the table with these frequencies.
Number
0
1
2
3
4
5
6
7
8
9
Frequency
9999
10 137
9908
10 025
9971
10 026
10 029
10 025
9978
9902
We are asked to display the given data using a bar graph. Let's recall that in this type of graph each bar represents a specific category. Here, each bar represents one number.
Looking at the graph, we can see that bars are approximately the same height because the differences between frequencies are relatively small.
Now we are asked to display the data in a circle graph. This type of graph shows data as parts of a whole. This means that we need to divide each frequency by the number of analyzed digits — 100 000. Let's do this!
Number
Frequency
Percentage
0
9999
9999/100 000=9.999 %
1
10 137
10 137/100 000=10.137 %
2
9908
9908/100 000=9.908 %
3
10 025
10 025/100 000=10.025 %
4
9971
9971/100 000=9.971 %
5
10 026
10 026/100 000=10.026 %
6
10 029
10 029/100 000=10.029 %
7
10 025
10 025/100 000=10.025 %
8
9978
9978/100 000=9.978 %
9
9902
9902/100 000=9.902 %
We can see that percentages vary from about 9.9 % to 10.1 %. This suggests that all parts of our circle graph will be of a similar size.
Now we want to decide which of the data displays is more appropriate for the given situation.
Bar Graph vs. Circle Graph
Here, the researchers wanted to analyze the frequency of each number. In case of showing frequencies, a bar graph is a more appropriate display of data compared to a circle graph.
Let's take a look at the bar graph we made in Part A.
As we said before, the bars have approximately the same heights. Checking the numbers of the y-axis, each number occurred approximately 10 000 times in the first 100 000 digits of π. A distribution in which bars are of approximately the same height are said to be uniform. In other words, the data set has a uniform distribution.
