This competency includes about 8 multiple-choice questions which makes up about 10% of the entire exam.
These questions test your knowledge of probability and statistics, including counting principles, bias, expected value, charts and graphs, linear regression, and statistical measures.
Here are some concepts you definitely need to know.
Measures of Central Tendency
Measures of central tendency help us to determine how data is distributed by identifying a single value at roughly the center of the data. We will consider several measures of central tendency below.
The mean of a data set is the average value of a data set. This can be found by adding together all of the values and dividing by the total number of values.
The mode of a data set is the value that occurs most frequently in the data set. It is possible to have more than one mode in a data set if several values occur the most.
The median of a data set is the middle value in the set. If there is an even number of data points, there will not be an exact middle. In this case, the median is found by taking the average of the two data points closest to the middle.
For example, suppose that the ages for a group of ten students were collected and are listed below:
9, 11, 13, 11, 8, 7, 13, 9, 9, 12
The mean of this data set can be found by adding all of these ages together and dividing by 10, since there are 10 students:
Mean = (9+11+13+11+8+7+13+9+9+12) / 10 = 10.2
To find the mode and median of a data set, it is helpful to reorder the set from lowest to highest:
7, 8, 9, 9, 9, 11, 11, 12, 13, 13
Now, we can see that the mode of the data set is 9, since 9 occurs 3 times, which is more than any other data point.
Since the data set has an even number of values, there are two values in the middle: 9 and 11. To find the median, you must average 9 and 11; therefore, the median of the data set is 10.
Permutations and Combinations
A permutation is an arrangement of items that occurs when the order of the items makes a difference, and no item is used more than once.
Usually, we are concerned with how many permutations can be made from a collection of items.
The formula for the number of permutations of n things taken r at a time is denoted as nPr:
For example, suppose that you have 20 different people in your family, and you want to know how many ways there are to fill 5 seats on a couch, where the order of the people on the couch matter.
So, there are 1,860,480 different ways to fill the 5 seats.
A combination is a collection of items in which the order does matter, but no item is used more than once.
The formula for the number of combinations of n things taken r at a time is denoted as nCr:
For example, suppose you have a 52 card deck, and you deal 7 cards. How many different hands of 7 cards are possible? Since it does not matter what order the cards are in for your hand, we need to count the combinations of 52 things taken 7 at a time:
So, there are 133,784,560 possible combinations of 7 cards chosen from the deck.