Summarizing Frequency of Events
According to the "phenomenon of red shirts" in the original series of Star Trek, a character wearing a red shirt was more likely to die than a person wearing a different color shirt. The original Star Trek was on the air for three seasons.
During those three seasons, 59 accidents occurred. There are four kinds of shirt: yellow, blue, engineering smock and red.
The frequency of accidents was as follows.
Season 1: 4 yellow, 3 blue, 4 engineering smocks and 6 red
Season 2: 2 yellow, 2 blue, 0 engineering smocks and 11 red
Season 3: 1 yellow, 0 blue, 0 engineering smocks and 26 red
Q Create a frequency table and a histogram to illustrate the data
There are data for each of the three seasons so we should include this in the frequency table and histogram to give all the information.
i) A frequency table is a table giving the number of occurrences of events.
Frequency table showing frequency of accidents, per season of Star Trek episodes in the original series, involving characters wearing different colored shirts
Frequency per season
shirt color 1 2 3 total
yellow 4 2 1 | 7
blue 3 2 0 | 5
engineering smock 4 0 0 | 4
red 6 11 26 | 43
total 17 15 27 59
Looking at this we can see that there are considerably more accidents involving characters wearing red shirts than any other color, and indeed all the other colors put together. We can also see that these accidents in red shirts were mainly in season 3 (26 versus 17 in seasons 1 and 2 put together). Finally, we can also see that there were more accidents in general in season 3 than in seasons 1 and 2, and that these were mainly characters in red shirts. The accidents in season 2 were also mainly of characters in red shirts, but the difference between red and the other colors is less obvious in season 1.
ii) A histogram is a bar chart that graphs the freqency of occurences of events. It is really then a pictorial representation of a frequency table. Since we are interested in the number of accidents per season as well as the total, we can divide the bars pertaining to accidents involving characters wearing a particular color shirt into three sections. This will show the proportions of the frequencies of the 4 colors which may also be of interest.
Histogram showing frequency of accidents in the original Star Trek series involving characters wearing different colored shirts. The frequencies for each of the shirt colors are divided up into those relating to seasons 1, 2 and 3 respectively (see hist.pdf attached)
We can see from the graph that most accidents involve characters in red shirts, and these accidents are mainly in season 3. It is harder than in the frequency table to see that there were more accidents in season 3 than in seasons 1 and 2 respectively. But, we can see that the accidents in both of seasons 2 and 3 were mainly involving characters wearing red shirts, and that this pattern cannot be seen in season 1. In general, the graph gives a good visual display of the data, but it is hard to decipher the exact number of events in each colored block without looking more closely.