Today's soundtrack is Suffocation: ...Of the Dark Light.
Today's activity was supposed to be "30 Minutes of Game Development," but my son has just discovered the joy of playing racing games with my steering wheel on my desktop computer, so I'm relegated to the other side of the desk today. Thus, I'm continuing on to the 19th chapter of Basic Math & Pre-Algebra For Dummies, "Figuring Your Chances: Statistics and Probability."
According to the introduction to the chapter, statistics and probability are important to "business, biology, city planning, politics, meteorology, and many more areas of study[, including] physics" (p. 259).
Statistics
"Statistics is the science of gathering and drawing conclusions from data" (p. 260), and "[a]n individual statistic is a conclusion drawn from this data" (p. 260). There are two kinds of data: qualitative data and quantitative data. Qualitative data gives us data that can't be measured with numbers; quantitative data gives us numeric information. We can use qualitative data in a quantitative way; for example, qualitatively we could do a survey and find out what colour eyes people have, then we could quantify that data and find out what percentage has brown eyes.
Now we get into averages: the mode "tells you the most popular answer to a statistical question" (p. 263), which isn't necessarily the highest percentage! For example, if I ask a group of ten teenagers what colour their car is, and three of them have no car, two have red cars, two have blue cars, two have silver cars, and one has a black car, the mode would be "no car," even though less than half of them have no car. If the student with a black car in the previous example had a red car instead, then we would have two modes: "no car" and "red car." Having multiple modes isn't a problem.
The mean refers to "the most commonly used average"; it's the regular average that we talk about. An example of finding a mean would be if I asked a group of five people what year their car is, and the answers were 1995, 2007, 2008, 2017, and 2018, I would add the numbers together and divide by the number of respondents: the answer is 2009, which is the mean of the respondents' year of car.
A warning given in the book is that the mean can be misleading if you have a result with lots of very high numbers and lots of very low numbers. For example, if I was in a muscle car club of 20 people, 8 of whom had brand-new 2018 Mustangs, 9 of whom had 1980 Dodge Challengers, and 3 of whom had 1969 Murcury Cyclones, I could tell you that the average person in the car club owned a 1993 muscle car, that really wouldn't be an accurate representation of the car club, would it?
The median is a good way to represent an average if there are a few outliers but lots in the middle area. We arrange the numbers from lowest to highest and pick the middle one to represent the median. If there are two numbers in the middle (an even number of subjects), find the mean of those two numbers; the result will be the median.
Probability
Probability is how likely an even is. We determine them by making a fraction: Probability equals successes divided by total possible outcomes. The probability of a coin toss landing on heads is P = 1/2. The probability of a dice landing on the number 5 is 1/6. The probability of picking a queen in a pack of cards is 4/52 (because there are four queens in the pack of 52 cards).
If we are figuring out the same thing but with multiple objects at the same time - say, tossing four coins and wondering what the probability is that all of them will be tails - to find our denominator, we say that the total number of outcomes per object times the number of objects is our total outcomes.
