SAT II Math I : Data Analysis and Statistics

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #61 : Data Analysis And Statistics

Find the median of the set:

\(\displaystyle 19, 27, 29, 30, 32, 33, 33, 34, 38, 40, 40, 40, 58\)

Possible Answers:

\(\displaystyle 33.5\)

\(\displaystyle 34\)

\(\displaystyle 33\)

\(\displaystyle 32.5\)

Correct answer:

\(\displaystyle 33\)

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle.

\(\displaystyle 19, 27, 29, 30, 32, 33, {\color{Red} 33}, 34, 38, 40, 40, 40, 58\) 

This gives us a final answer of 33 for the median.

Example Question #32 : Median

FInd the median of the set:

\(\displaystyle 4, 5, 6, 12, 15, 18, 19, 23, 26, 27, 31, 39, 41\)

Possible Answers:

\(\displaystyle 23\)

\(\displaystyle 18\)

\(\displaystyle 23\)

\(\displaystyle 19\)

Correct answer:

\(\displaystyle 19\)

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle.

\(\displaystyle 4, 5, 6, 12, 15, 18, {\color{Red} 19}, 23, 26, 27, 31, 39, 41\) 

This gives us a final answer of 19 for the median.

Example Question #31 : Median

Find the median of the set:

\(\displaystyle 12, 15, 16, 24, 25, 31, 36\)

Possible Answers:

\(\displaystyle 20\)

\(\displaystyle 25\)

\(\displaystyle 16\)

\(\displaystyle 24\)

Correct answer:

\(\displaystyle 24\)

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle.

\(\displaystyle 12, 15, 16, 24, 25, 31, 36\) 

This gives us a final answer of 24 for the median.

Example Question #32 : Median

Find the median of the set:

\(\displaystyle 15, 24, 27, 28, 28, 39, 44, 47, 61, 77, 88\)

Possible Answers:

\(\displaystyle 41\)

\(\displaystyle 28\)

\(\displaystyle 44\)

\(\displaystyle 39\)

Correct answer:

\(\displaystyle 39\)

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle.

 \(\displaystyle 15, 24, 27, 28, 28, {\color{Red} 39}, 44, 47, 61, 77, 88\)

This gives us a final answer of 39 for the median.

Example Question #33 : Median

Find the median of the set:

\(\displaystyle 14, 22, 22, 31, 32, 35, 36, 37, 39, 41, 42, 48, 50, 58, 63\)

Possible Answers:

\(\displaystyle 37\)

\(\displaystyle 36\)

\(\displaystyle 35\)

\(\displaystyle 39\)

Correct answer:

\(\displaystyle 37\)

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle.

\(\displaystyle 14, 22, 22, 31, 32, 35, 36, {\color{Red} 37}, 39, 41, 42, 48, 50, 58, 63\)

This gives us a final answer of 37 for the median.

Example Question #34 : Median

Find the median of the following number set:

\(\displaystyle 14,15,76,345,222,976,300,117,236,426\)

Possible Answers:

\(\displaystyle 754\)

\(\displaystyle 229\)

\(\displaystyle 599\)

\(\displaystyle 272.7\)

Correct answer:

\(\displaystyle 229\)

Explanation:

Find the median of the following number set:

\(\displaystyle 14,15,76,345,222,976,300,117,236,426\)

Recall that the median is the middle value of a number set when it is arranged in ascending order. So we must begin by arranging the set in ascending order.

\(\displaystyle 14,15,76,117,{\color{DarkOrange} 222,236},300,345,426,976\)

In this case, because we have an even number of terms, we do not have a single middle number. This means we need to take the average of the middle two terms to find our median.

\(\displaystyle Median=\frac{222+236}{2}=229\)

So our answer is 229.

Example Question #35 : Median

Find the median:  \(\displaystyle a=[-5,-1-1,0,-2,-9]\)

Possible Answers:

\(\displaystyle \textup{There is no median.}\)

\(\displaystyle -\frac{1}{2}\)

\(\displaystyle -\frac{3}{2}\)

\(\displaystyle -1\)

\(\displaystyle -2\)

Correct answer:

\(\displaystyle -\frac{3}{2}\)

Explanation:

First regroup all numbers in chronological order.

\(\displaystyle a=[-5,-1-1,0,-2,-9] = [-9,-5,-2,-1,-1,0]\)

Since there is an even amount of numbers in the dataset, 6 numbers total, the median will be the average of the third and fourth numbers.

Find the mean of the two numbers.

\(\displaystyle \frac{-2-1}{2}= -\frac{3}{2}\)

Example Question #36 : Median

Find the median of the following data set:

\(\displaystyle 1,43,117,42,2952,54,18,97,112,23\)

Possible Answers:

\(\displaystyle 54\)

\(\displaystyle 325\)

\(\displaystyle 2951\)

\(\displaystyle 117\)

Correct answer:

\(\displaystyle 54\)

Explanation:

Find the median of the following data set:

\(\displaystyle 1,43,117,42,2952,54,18,97,112,23,117\)

To find the median, we should first put our numbers in increasing order:

\(\displaystyle 1,18,23,42,43,54,97,112,117,117,2952\)

Next, the median will simply be the number in the middle. 

We have 11 terms, so our median will be the 6th term in the sequence:

\(\displaystyle 1,18,23,42,43,{\color{DarkBlue} 54},97,112,117,117,2952\)

So 54 is our median

Example Question #37 : Median

Find the median of this data set:

\(\displaystyle 145,57,223,76,453,123,979,57,76,233,435,76\)

Possible Answers:

\(\displaystyle 922\)

\(\displaystyle 244\)

\(\displaystyle 57\)

\(\displaystyle 134\)

Correct answer:

\(\displaystyle 134\)

Explanation:

Find the median of this data set:

\(\displaystyle 145,57,223,76,453,123,979,57,76,233,435,76\)

To begin, let's put our numbers in increasing order:

\(\displaystyle 57,57,76,76,76,123,145,223,233,435,453,979\)

Next, find the median by finding the number in the middle of  the data set. If there are two numbers in the middle, then find their average:

\(\displaystyle 57,57,76,76,76,{\color{Blue} 123,145},223,233,435,453,979\)

So, the median will be:

\(\displaystyle \frac{123+145}{2}=\frac{268}{2}=134\)

 

Example Question #38 : Median

Find the median of the following data set:

\(\displaystyle 66,123,44,78,99,67,143,44,107,12,578,12,67,367,44\)

Possible Answers:

\(\displaystyle 566\)

\(\displaystyle 44\)

\(\displaystyle 114\)

\(\displaystyle 67\)

Correct answer:

\(\displaystyle 67\)

Explanation:

Find the median of the following data set:

\(\displaystyle 66,123,44,78,99,67,143,44,107,12,578,12,67,367,44\)

Let's begin by putting our data in increasing order:

\(\displaystyle 12,12,44,44,44,66,67,67,78,99,107,123,143,367,578\)

Now, the median should be pretty straightforward to find.

The median will simply be the number in the middle of all the terms. 

In this case, it is the number in red below

\(\displaystyle 12,12,44,44,44,66,67,{\color{Red} 67},78,99,107,123,143,367,578\)

So our answer is 67.

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