SAT Math : Statistics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #91 : Statistics

Craig has a jar full of loose change.  He has 20 quarters, 15 dimes, 35 nickels and 55 pennies.  If he orders them all from least to most valuable, what is the value of the median coin?

Possible Answers:

Correct answer:

Explanation:

The median is the coin which has an equal number of coins of lesser or equal value and greater or equal value on either side of it.  The median therefore falls to one of the nickels (62 quarters, dimes and nickels above it and 62 nickels and pennies below it).  The value of a nickel is 5 cents.

Example Question #92 : Statistics

A student decides to review all of his old tests from his math class in order to prepare for the upcoming exam.  The student decides that any exam in which he  received a 94% or better he should be able to skip since he understood the material well, but he will review the rest.  The first 7 tests are scored out of 50 points.  The rest are scored out of 40 points. In order, they got the following raw scores:

The student has 1 more test to add to this list. If he puts together all the tests he must review in order of percentile score, this final test is the median score.  Which of the following cannot be the raw score of this final test?

Possible Answers:

Correct answer:

Explanation:

We first remove any 94%+ scores.  For tests scored out of 50, a 94% is a 47.  Thus anything 47 or greater will be removed.  We see that this leaves us with:

For the second half, we have tests scored out of 40.  94% of 40 gives us 37.6, thus we will only remove tests that were a 38 or better.  This leaves us with:

Now we have to convert them to percentiles.  We end up with the lists as follows. The raw scores are in parentheses:

We then order it by percentile (removing raw scores, as they are unnecessary):

We notice that the median must be between the 78 and the 87.5 percentile scores. 31 out of 40 gives us 77.5%, which is below the score associated with an earlier test.  Thus this cannot be the answer.  The remaining 4 scores are all higher than 78%, and the largest of them is equal to 87.5 (the highest bound). 

Example Question #3 : How To Find Median

67, 73, 85, 83, 80, 73, 94, 65, 80, 73, 98, 59, 76

The list above shows a ninth grader's grades for the academic year. What is the difference between the median and the mode of these grades?

Possible Answers:

Correct answer:

Explanation:

To find the median, sort the numbers from smallest to largest:

59, 65, 67, 73, 73, 73, 76, 80, 80, 83, 85, 94, 98

The median is the middle value in a list of numbers, it is the number separating the higher half of a data sample or a list of numbers from the lower half.

The median of the grades is 76.

The mode is the value occurring most often. The most occurring value in the list of numbers given is 73. So, the mode is 73.

Example Question #93 : Statistics

What is the median for the following test scores of students on a test:

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, the tests need to be organized from smallest to largest. 

The median is the middle number in the set of data. From here the smallest and the largest numbers can be "crossed off" until one number remains. This gives the correct answer of 88. 

Example Question #92 : Statistics

Find the median of the following set:  

Possible Answers:

Correct answer:

Explanation:

Reorder all the numbers from smallest to largest.

Since there are four numbers in this set, we will average the second and third number in the set to find the median.

The median is .

Example Question #22 : Median

The following represent speeds of passing cars collected by a surveillance camera:

What is the median of the speeds? 

Possible Answers:

Correct answer:

Explanation:

The median of a set of numbers is the number that falls in the middle of the set. 

If we reorder the numbers from least to greatest, we get:

The number that falls in the middle of this set is the fourth number, which is 

Example Question #94 : Statistics

Find the median of the following set of numbers:

1,5,14,17,22,23,23

Possible Answers:

Correct answer:

Explanation:

To solve, simply find the middle number. Since the numbers are already ordered from smallest to largest, we can easily do this. 7 numbers means the 4th one from either end will be the middle. Thus, our answer is 17.

 

Example Question #24 : Median

A set of six numbers is listed below.

 is an even integer that is greater than 10 but less than 30.  If  is added to the set of numbers, all of the following could be the median except: 

Possible Answers:

Correct answer:

Explanation:

The median is the number that falls in the middle of a set of numbers when they are placed in order from least to greatest. 

With an odd number of numbers in this set, you always have one of the values in the set as your median (as opposed to the average of the two middle values when you have an even number of numbers in a set). Therefore, because all of the numbers in this set are integers, you cannot have 24.5 as the median 

Example Question #91 : Statistics

The heights of the members of a basketball team are inches. The mean of the heights is . Give the median of the heights.

Possible Answers:

Correct answer:

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

 

 

Where:

 

is the mean of a data set, indicates the sum of the data values and is the number of data values. So we can write:

 

 

In order to find the median, the data must first be ordered:

 

 

Since the number of values is even, the median is the mean of the two middle values. So we get:

 

 

 

Example Question #95 : Statistics

The table below shows the number of college graduates per 2 months

 

 

Which 2 month period had the most college graduates?

 

Possible Answers:

Correct answer:

Explanation:

In order to answer this question, we need to add each column up and see what column is the largest.

It looks like that the  2 month period has the most college graduates.

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