Next, let’s take a look at some data analysis concepts and discuss how they might appear on the Quantitative Reasoning portion of the GRE.
Mean, Median, and Mode
Next, we will review mean, median, and mode, which are measures of central tendency. Let’s use an example data set. The list below gives the weights of 9 dogs.
Weight (in pounds): 64, 46, 34, 70, 15, 14, 45, 75, 70
First, we will order the list from least to greatest (ordering the list from greatest to least is also effective).
Weight (in pounds): 14, 15, 34, 45, 46, 64, 70, 70, 75
Mean: Sum divided by the total. 433 pounds ÷ 9 dogs = 48.111
Median: The value in the center of the ordered list. 46
Mode: The value which occurs most often. 70
Next, we’ll review some concepts related to probability.
Probability of a Single Event
Probability refers to the likelihood that an event will occur. For example, the probability of a coin landing in the “heads” position is 0.5. In other words, there is a 50% chance of this outcome. No matter how many times the coin is flipped, the probability of this outcome stays the same.
The probability (P) of an event (E) can be expressed as:
So, the probability of drawing a specific card from a deck of 52 cards is:
(P)E = 1 / 52 = which is about .019 or 1.9%
Probability of Compound Events
Now, think about the probability of drawing a specific card and then drawing a second specific card. This scenario is a little bit different because it deals with compound events.
If a card is drawn from a deck and replaced before a second card is drawn, each time a card is drawn is an independent event. These outcomes do not affect each other.
Imagine that you have a bag of 5 marbles and each marble in the bag is a different color. You also have a package of 10 candies and each candy is a different flavor. First, you remove a marble, then you remove a candy.
Removing the marble has no effect on what type of candy you remove and vice versa.
So, what is the probability of drawing a purple marble from the bag, then drawing a strawberry-flavored candy from the package? The first event, drawing the marble, may be expressed as P(A). The second event, drawing the candy, may be expressed as P(B).
P(A and B) = P(A) ∙ P(B)
Probability of drawing a purple marble (1 / 5) and a strawberry candy (1 / 10):
P(A and B) = (1 / 5) ∙ (1 / 10) = (1 / 50) = 2%
There is a 2% chance of achieving these two outcomes.
Just as there are independent events, there are dependent events. For example, if you draw a card from a deck and do not replace it before drawing another, the first event affects the second event.
Conditional probability may be expressed as:
P(A and B) = P(A) ∙ P(B|A)
Let’s solve an example problem.
Freya randomly draws two cards from a deck of 52 cards without replacing the first card. What is the likelihood that both cards she draws are queens?
P(A and B) = P(A) ∙ P(B|A)
P(A) = (4 / 52)
P(B|A) = ∙ ( 3 / 51) Notice that there are now fewer cards!
P(A and B) = (4 / 52) ∙ (3 / 51) = (12 / 2562) = (1 / 221) = about .0045
We can round .0045 to determine that Freya has about a .5% chance of drawing two queens.
Tables and Graphs
Often, data appears in the form of tables and graphs the Quantitative Reasoning measure. Let’s review those concepts now.
You can see an example of a frequency table below. This table shows the quiz scores of a group of students.
Think back to measures of central tendency. If you were asked to find the median score, you would list all of the scores in order from highest to lowest (or vice versa).
70, 74, 77, 80, 83, 83, 86, 86, 86, 90, 90, 90, 90, 92, 94, 94, 98
Based on the table, you can determine that 86 is the median score. Remember to refer to both sides of a frequency table. For this example, it is important to know how many students made each of the grades listed.
Below, you can find an example of a bar graph as well as an example of a histogram.
Notice that the information in both the histogram and the bar graph is the same. The difference is that the bars on a histogram touch.
Let’s look at a second bar graph now and answer an example question.
The following bar graph shows the number of novels a public library purchased over the course of three months.
There were _____ more novels purchased in February than in April.
For this question, we can ignore the middle bar, which represents March. In February, the library purchased 40 novels and in April, the library purchased 35 novels. So that’s a difference of 5 novels.
And that’s some basic info about the Quantitative Reasoning measure.