Algebra 1 : How to find median

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #21 : How To Find Median

What is the median?

\(\displaystyle 2, 4, 5, 6, 9\)

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 4\)

\(\displaystyle 5\)

\(\displaystyle 2\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 5\)

Explanation:

To find median, we need to find the middle number in the set. There are five numbers, so the middle number is basically third in the set. That number is \(\displaystyle 5\)

Example Question #22 : How To Find Median

What is the median?

\(\displaystyle 16, 5, 2, 7, 18\)

Possible Answers:

\(\displaystyle 18\)

\(\displaystyle 2\)

\(\displaystyle 16\)

\(\displaystyle 7\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 7\)

Explanation:

To find median, we should arrrange the numbers in increasing order. That would be \(\displaystyle 2, 5, 7, 16, 18\). Next, since there are five numbers, the middle number is the third. That value is \(\displaystyle 7\)

Example Question #223 : Statistics And Probability

What is the median?

\(\displaystyle 1, 3, 6, 8, 9, 17\)

Possible Answers:

\(\displaystyle 8.5\)

\(\displaystyle 7\)

\(\displaystyle 8\)

\(\displaystyle 6\)

\(\displaystyle 6.5\)

Correct answer:

\(\displaystyle 7\)

Explanation:

To find median, we count the numbers in the set. There are six. Since six is an even number, we go to the two middle numbers which are \(\displaystyle 6\) and \(\displaystyle 8\). We average the two numbers to get \(\displaystyle 7\)

Example Question #23 : How To Find Median

What is the median?

\(\displaystyle -25, -14, -3, 1, 5, 6\)

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 1\)

\(\displaystyle -3\)

\(\displaystyle -1\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle -1\)

Explanation:

To find median, we count the numbers in the set. There are six. Since six is an even number, we go to the two middle numbers which are \(\displaystyle -3\) and \(\displaystyle 1\). We average the two numbers to get \(\displaystyle -1\)

Example Question #301 : Basic Arithmetic

What is the median?

\(\displaystyle -9, -22, -14, -6, 9, 0\)

Possible Answers:

\(\displaystyle -7.5\)

\(\displaystyle -9\)

\(\displaystyle -6\)

\(\displaystyle 9\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle -7.5\)

Explanation:

To find median, we must arrange the numbers in increasing order. The larger the negative value, the smaller it is. We get \(\displaystyle -22, -14, -9, -6, 0, 9\).Then, we count the numbers in the set. There are six. Since six is an even number, we go to the two middle numbers which are \(\displaystyle -9\) and \(\displaystyle -6\). We average the two numbers to get \(\displaystyle -7.5\)

Example Question #23 : How To Find Median

What is the median?

\(\displaystyle -2.4, -3.5, 6.8, 4.6, -98.3, -6.2, -2.4\)

Possible Answers:

\(\displaystyle 5.8\)

\(\displaystyle -98.3\)

\(\displaystyle 4.6\)

\(\displaystyle 5.7\)

\(\displaystyle -2.4\)

Correct answer:

\(\displaystyle -2.4\)

Explanation:

To find median, we must arrange the numbers in increasing order. The larger the negative value, the smaller it is. We get \(\displaystyle -98.3, -6.2, -3.5, -2.4, -2.4, 4.6, 6.8\).Then, we count the numbers in the set. There are seven. The middle number is \(\displaystyle -2.4\)

Example Question #25 : How To Find Median

If the median must be a value below \(\displaystyle 5\), what could be a possible value of \(\displaystyle x\)?

\(\displaystyle x, 4, 2, 8, 9\)

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 6\)

\(\displaystyle 10\)

\(\displaystyle 4.5\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 4.5\)

Explanation:

To ensure the median is below \(\displaystyle 5\), we need to arrange so that \(\displaystyle x\) is the middle. So we have \(\displaystyle 2, 4, x, 8, 9\). The only value below \(\displaystyle 5\) is \(\displaystyle 4.5\)

Example Question #26 : How To Find Median

If the median is between \(\displaystyle 0\) and \(\displaystyle 1\) inclusive, what value of \(\displaystyle x\) can it NOT be?

\(\displaystyle -3, -5, -1, 4, 5, x\)

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle 2\)

\(\displaystyle 4\)

\(\displaystyle 1.5\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 4\)

Explanation:

To find median, let's arrange the numebers in increasing order so that we can get a median between \(\displaystyle 0\) and \(\displaystyle 1\) inclusive. We have \(\displaystyle -5, -3, -1, x, 4, 5\). This works best since \(\displaystyle -1\) when added to a value and averaged will fall in our target interval. The equation to find the median for an even set will be \(\displaystyle \frac{-1+x}{2}=0\) or \(\displaystyle \frac{-1+x}{2}=1\). The reason for this is to find the minimum and maximum value of \(\displaystyle x\). For the first equation, we cross multiply and get \(\displaystyle -1+x=0\) or \(\displaystyle x=1\). The second equation we get \(\displaystyle -1+x=2\) or \(\displaystyle x=3\). The value that's not in this range is \(\displaystyle 4\)

Example Question #24 : How To Find Median

If the average of two numbers is \(\displaystyle 7\), what is the median of the two numbers?

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 0\)

\(\displaystyle 14\)

\(\displaystyle 7\)

Impossible to tell

Correct answer:

\(\displaystyle 7\)

Explanation:

When finding median of even numbers in the set, you take the average of the two middle numbers to find median. Since \(\displaystyle 2\) is an even number and we know the average, that value is the same as the median. Answer is \(\displaystyle 7\)

Example Question #25 : How To Find Median

What is the median price of the cars?

Q9

Possible Answers:

\(\displaystyle 20000\)

\(\displaystyle 17500\)

\(\displaystyle 15000\)

\(\displaystyle 7\)

\(\displaystyle 25000\)

Correct answer:

\(\displaystyle 20000\)

Explanation:

If we count the total number of cars, we get \(\displaystyle 15\). The middle number is \(\displaystyle 8\). When going in order from smallest to largest, number \(\displaystyle 8\) falls in the \(\displaystyle 20000\) category so that's the answer. 

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