Advanced I Statistics (7-9 old curriculum) Flashcards
mean
the average
mean = sum of all values / number of all values
median
the middle number of a data set
If there is an even amount of data, then take the average of the two middle numbers
range
the maximum data value minus the minimum data value
outlier
a datum that is surprisingly far away from the rest of the data
In later courses you will define just how far this point must be to be an outlier, but that is beyond the scope of this grade level (this is first taught in university or AP Statistics class in grade 12 which is equivalent to first year university)
central tendency
There are different measures of central tendency, and they hope to show where the centre of the data lies.
Mean, median, and mode are measures of central tendency.
Use the median when there are outliers. Use the mode when you are working with categories and do not have numbers. Use mean when your data is not skewed and when there are no outliers.
probability
the likelihood of something happening
Probability = total favourable outcomes / total possible outcomes
total possible outcomes is also known as the sample space
Make sure that you know how to make a tree diagram of all total outcomes. Then highlight those outcomes that satisfy the thing you are concerned about (the favourable outcomes). Then the fraction of highlighted to total outcomes will give you the probability that the favourable outcome will occur.
Usually probability is represented as a percentage, so make sure you are familiar with converting fractions to a percent.
Finding the total possible outcomes can be tricky: this can always be done with a tree diagram, but it would be huge with some problems, thus you will notice that there are other mathematical ways that have been developed to calculate the total possible outcomes. You may need to see several examples before you can start to understand all the possible math equations involved given any probability question. This is explored at length in the grade 12 curriculum. For grade 7-9 concern yourself with independent event probabilities since you are not required to understand dependent events until much later.
Total possible outcomes for independent events can be calculated by this formula:
outcomes = n ^ r where n is the number of options available for each of the rounds, and r is the rounds This is assuming that you care about the order so A A A B is different from B A A A for example and those would each be a separate outcome
For example: if you have tiles in a bag each with a letter of the alphabet, and you pick 4 of them but always replace the tile back in the bag, what are the possible outcomes?
outcomes = 26 ^ 4
This is independent probability since we replace the tile in the bag again so each round we have 26 choices.
In grade 12 you will explore when you do not put the tile back in the bag.
Once you have the total outcomes, you can look at the favourable outcomes in a similar way. But to keep it simple here I will ask, what is the probability that you make A A A A happen in the situation above?
Probability = 1 / 26^4 since A A A A is only one highlighted event
Probability = 0.000002188298729
Probability = 0.0002%
Notice how highly unlikely you would have this occur
experimental probability
found by simulation and doing many different trials to see how often certain outcomes tend to occur in the experiment
theoretical probability
found by performing a calculation of probability but not looking at the actual events that occurred over many trials
sample space
Also known as outcomes.
The set of all possible outcomes.
The amount of ending points on your tree diagram.
tree diagram
E.g. draw a tree diagram of A B C tiles that we can pick out of a bag assuming that order matters and that the tiles are coming from an infinite sample set (we replace the tiles back in the bag after each time we pick)
independent events so we can use outcomes = n ^ r
independent events
Where the outcome of one event does not affect the potential outcomes of the next.
The probability questions you will see should be based on independent events at this level.
This is why you are able to use the formula outcomes = n^r
To contrast, this is what it is like when you do not have independent events:
you would be using another formula that allows you to multiply by successively lower numbers such as something like this:
7x6x5x4 and this would be because after picking the first tile from the bag, you are not allowed to pick it again.
The concept just mentioned here has way more to it and is introduced in math 30-1, so don’t worry about it now. (If you are in math 30-1 then you of course would need to know factorials, permutations, and combinations in order to answer your questions, in addition to the independent events formula)
Define bias
prejudice in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair
In statistics this means that we are asking bad questions or representing data in a way that is misleading or a variety of other things that could unfairly lead the people to believe something that is not true. Make sure that you are representing data in an appropriate manner.
Define ethics
moral principles
When posing questions to others we must remain ethical. We also must choose who we are asking ethically. We must make sure to treat everyone according to the highest moral principles possible.
What are some influences on how you choose to collect data?
time available to collect answers
cost
timing of the question to current events
privacy
cultural sensitivity
trying to be ethical
trying to eliminate bias
population vs. sample
sample is the portion, population is the whole
We sample the population to try to reduce costs instead of asking questions to everyone. Sometimes this leads to us not being able to extrapolate outside of the sample; to extrapolate and make conclusions on the population you would need to take a simple random sample, and this is much tougher than you think. You would need to look at the demographics of who you are sampling and prove that it matches the demographics and proportions in the population.
