Algebra II : Data Properties

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #53 : Data Analysis And Statistics

Find the median of the set:

\displaystyle 2, 3, 5, 8, 13, 21, 34, 55

Possible Answers:

\displaystyle 8

\displaystyle 10.5

\displaystyle 11.5

\displaystyle 13

Correct answer:

\displaystyle 10.5

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 even amount of numbers in the set meaning there are two "middle numbers"- 8 and 13. In order to find the median we take the average of 8 and 13:

\displaystyle \frac{8+13}{2}=10.5

Example Question #54 : Data Analysis And Statistics

Find the median of the set:

\displaystyle 15, 15, 19, 21, 22, 24, 26, 27, 29, 31, 33, 36

Possible Answers:

\displaystyle 24

\displaystyle 27

\displaystyle 26

\displaystyle 25

Correct answer:

\displaystyle 25

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 even amount of numbers in the set meaning there are two "middle numbers"- 24 and 26. In order to find the median we take the average of 24 and 26:

\displaystyle \frac{24+26}{2}=25

Example Question #55 : Data Analysis And Statistics

Find the median of the set:

\displaystyle 32, 33, 33, 34, 35, 37, 38, 41, 42, 45, 47

Possible Answers:

\displaystyle 38

\displaystyle 35

\displaystyle 36

\displaystyle 37

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 32, 33, 33, 34, 35, {\color{Red} 37}, 38, 41, 42, 45, 47

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

Example Question #331 : Algebra Ii

Find the median of the set:

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

Possible Answers:

\displaystyle 34

\displaystyle 33.5

\displaystyle 32.5

\displaystyle 33

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 #332 : Algebra Ii

FInd the median of the set:

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

Possible Answers:

\displaystyle 18

\displaystyle 23

\displaystyle 19

\displaystyle 23

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 #333 : Algebra Ii

Find the median of the set:

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

Possible Answers:

\displaystyle 20

\displaystyle 24

\displaystyle 16

\displaystyle 25

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 #334 : Algebra Ii

Find the median of the set:

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

Possible Answers:

\displaystyle 44

\displaystyle 41

\displaystyle 28

\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 #335 : Algebra Ii

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 35

\displaystyle 39

\displaystyle 36

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 #239 : Data Properties

Find the median of the following number set:

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

Possible Answers:

\displaystyle 229

\displaystyle 272.7

\displaystyle 599

\displaystyle 754

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 -\frac{3}{2}

\displaystyle -1

\displaystyle -\frac{1}{2}

\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}

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