PSAT Math : Data Analysis
Study concepts, example questions & explanations for PSAT Math
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Example Questions
Example Question #1548 : Psat Mathematics
Set A:
Set B:
One letter is picked from Set A and Set B. What is the probability of picking two consonants?
Set A:
Set B:
In Set A, there are five consonants out of a total of seven letters, so the probability of drawing a consonant from Set A is 
In Set B, there are three consonants out of a total of six letters, so the probability of drawing a consonant from Set B is 
The question asks for the probability of drawing two consonants, meaning the probability of drawing a constant from Set A and Set B, so probability of the intersection of the two events is the product of the two probabilities:
Example Question #52 : Calculating Discrete Probability
Set A:
Set B:
One letter is picked from Set A and Set B. What is the probability of picking at least one consonant?
Set A:
Set B:
In Set A, there are five consonants out of a total of seven letters, so the probability of drawing a consonant from Set A is 
In Set B, there are three consonants out of a total of six letters, so the probability of drawing a consonant from Set B is 
The question asks for the probability of drawing at least one consonant, which can be interpreted as a union of events. To calculate the probability of a union, sum the probability of each event and subtract the intersection:
The interesection is:
So, we can find the probability of drawing at least one consonant:
Example Question #42 : Data Analysis / Probablility
Set A:
Set B:
One letter is drawn from Set A, and one from Set B. What is the probability of drawing a matching pair of letters?
Set A:
Set B:
Between Set A and Set B, there are two potential matching pairs of letters: AA and XX. The amount of possible combinations is the number of values in Set A, multiplied by the number of values in Set B, 
Therefore, the probability of drawing a matching set is:
Example Question #164 : Data Analysis
In a particular high school, 200 students are freshmen, 150 students are sophomores, 250 students are juniors, and 100 students are seniors. Twenty percent of freshmen are in honors classes, ten percent of sophomores are in honors classes, twelve percent of juniors are in honors classes, and thirty percent of seniors are in honors classes.
If a student is chosen at random, what is the probability that that student will be a student who attends honors classes?
First calculate the number of students:
The probability of drawing an honors student will then be the total number of honors students divided by the total number of students attending the school:
Example Question #61 : Discrete Probability
In a particular high school, 200 students are freshmen, 150 students are sophomores, 250 students are juniors, and 100 students are seniors. Twenty percent of freshmen are in honors classes, ten percent of sophomores are in honors classes, twelve percent of juniors are in honors classes, and thirty percent of seniors are in honors classes.
If a student is chosen at random, what is the probability that that student will be a senior student and a student who does not attend honors classes?
First calculate the number of students:
The percentage of seniors that do not attend honors classes is:
Therefore, the probability of selecting a student who is a senior and one who does not attend honors classes is:
Example Question #101 : How To Find The Probability Of An Outcome
11 cards are placed into a box numbered 5 - 15. If one card is randomly drawn from the box, what is the probabiltiy that a prime number will be on the card?
4/11
2/5
6/11
1/2
3/5
4/11
Possible numbers 5,6,7,8,9,10,11,12,13,14,15 (11 total numbers)
Prime numbers are 5,7,11,13 (4 total prime numbers)
totalnumber of prime numbers/ total numbers in box
Answer = 4/11
Example Question #111 : Outcomes
Aaron, Gary, Craig, and Boone are sitting down in a row of four chairs. What is the probability that Aaron and Gary will be seated beside each other?
Consider first all of the possible ways the men may be arranged, which is
Now, consider all of the ways that Aaron and Gary could be seated beside each other; it may be easier to visualize by drawing it out:
- A G _ _
- G A _ _
- _ A G _
- _ G A _
- _ _ A G
- _ _ G A
As seen, there are six possibilities.
Finally, for each of these cases, Craige and Boone could be seated in one of two ways.
So the probability that Aaron and Gary will be seated beside each other is:
Example Question #1 : Drawing Conclusions From Graphs & Tables
Matt conducted a statistical experiment to determine the relationship between yearly salary earned and age. In this study, he assigned age (in years) as the independent variable, and yearly salary as the dependent variable. He drew a line of best fit and found a slope of 
Each year, a person's salary decreases by
Each month, a person's salary decreases by
Each year, a person's salary increases by
Each month, a person's salary increases by
Each year, a person's salary increases by
The slope of a line is the rate that a line increases or decreases. The question tells us that Matt looked at the relationship between age, in years; thus, the correct answer should include "each year", which eliminates the answer choices that include "each month". Finally the slope is 
Example Question #2 : Drawing Conclusions From Graphs & Tables
Mrs. Frame conducted a statistical experiment to determine the relationship between test grades and the number of hours her students spent studying. In this study, she assigned the number of hours spent studying as the independent variable, and the test grades (in percentages) were assigned as the dependent variable. She plotted the data on a scatter plot and drew a line of best fit. If the slope of the best fit line was 
Yes, the 
Yes ,the 
No, the 
Yes ,the 
Yes ,the
The equation of the best fit line will be in slope intercept form:
The question tells us that the slope is 
We had to convert our percentage into a decimal in order to multiple, but we need to change it back to a percent before we subtract so that we arrive at the correct answer because 
Example Question #542 : Grade 8
Mr. Miller conducted a statistical experiment to determine the relationship between final grades and the number of school days that his students missed. In this study, he assigned the number of missed school days as the independent variable, and the final grade was assigned as the dependent variable. He plotted his results on a scatter plot. If the results follow a linear relationship, what is a reasonable conclusion that could be found based these results?
A positive slope
A slope of
An undefined slope
A negative slope
A negative slope
We know, from attending school ourselves, that every day we learn something new in school. When a day of school is missed, there is a lot of catch up that needs to be done, but the teacher's instructions and lesson given each day can't be repeated the day you return, because the teacher has to move on with the rest of the class. If you missed a week of school, that's five days of lessons that were missed. Wouldn't it be challenging to catch up on what was missed, as well as learning what the teacher is currently teaching when you return? This would likely be challenging; thus, we can conclude that the more days of school missed, the lower a students final grade will be. As the number of days missed increases, the final grade will decrease; thus, the best fit line will have a negative slope.
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