Algebra 1 : How to find median

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #282 : Statistics And Probability

Refer to the following set of numbers:

\(\displaystyle 49, 51, 52, 52, 56, 57, 57, 57, 63\)

Find the median of the set.

Possible Answers:

\(\displaystyle 56\)

\(\displaystyle 51\)

\(\displaystyle 57\)

\(\displaystyle 52\)

Correct answer:

\(\displaystyle 56\)

Explanation:

The median of the set is the middle number. To find this, we order the numbers from smallest to greatest.

\(\displaystyle 49, 51, 52, 52, 56, 57, 57, 57, 63\)

In this case, the middle number is \(\displaystyle 56\)

Example Question #283 : Statistics And Probability

Refer to the following set of numbers:

\(\displaystyle 24,27,29,43,44,44,51,53,62,77,88\)

Find the median of the set.

Possible Answers:

\(\displaystyle 51\)

\(\displaystyle 53\)

\(\displaystyle 43\)

\(\displaystyle 44\)

Correct answer:

\(\displaystyle 44\)

Explanation:

The median of the set is the middle number. To find this, we order the numbers from smallest to greatest.

\(\displaystyle 24,27,29,43,44,44,51,53,62,77,88\)

In this case, the middle number is \(\displaystyle 44\)

Example Question #83 : How To Find Median

Mr. Black's algebra class took a quiz, and the scores that the students received were: \(\displaystyle 78, 45, 76, 34, 98, 87, 89, 94, 45, 62, 91\).

What was the median score that Mr. Black's class received on the quiz?

Possible Answers:

\(\displaystyle 45\)

\(\displaystyle 78\)

\(\displaystyle 64\)

\(\displaystyle 70\)

\(\displaystyle 73\)

Correct answer:

\(\displaystyle 78\)

Explanation:

To find the median of a set of numbers, we first must arrange the numbers in order from least to greatest. The scores on Mr. Black's quiz were \(\displaystyle 78, 45, 76, 34, 98, 87, 89, 94, 45, 62, 91\).

Placed in order, these scores were:

\(\displaystyle 34, 45, 45, 62, 76, 78, 87, 89, 91, 94, 98\)

Now that we have our numbers arranged in order, to find the median, all we need to do it find the number that is in the exact middle of the series. There were \(\displaystyle 11\) scores given for Mr. Black's quiz, so the 6th score in the series is our median - in this case \(\displaystyle 78\)

So, \(\displaystyle 78\) is the median score for Mr. Black's quiz.

Example Question #84 : How To Find Median

Frank is in a book club with \(\displaystyle 7\) other people. Their ages are \(\displaystyle 25, 36, 34, 21, 25, 18, 32, 27\).

What is the median age of the members of Frank's book club?

Possible Answers:

\(\displaystyle 25\)

\(\displaystyle 18\)

\(\displaystyle 24\)

\(\displaystyle 26\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 26\)

Explanation:

The find the median of a group of numbers, the first think we want to do is put the numbers in order from least to greatest.

The ages for everyone in Frank's book club are \(\displaystyle 25, 36, 34, 21, 25, 18, 32, 27\).

Put in order from least to greatest, the ages are:

\(\displaystyle 18, 21, 25, 25, 27, 32, 34, 36\)

Now that the numbers are in order, we can find the median. The median is the number that is in the middle of the sequence. Since there are \(\displaystyle 8\) ages total in our list, and \(\displaystyle 8\) is an even number, there is no single age that is in the exact middle of the list. So, to find the median, we will take the average (the 'mean') of the two middle ages. 

\(\displaystyle 25\) and \(\displaystyle 27\) and the two middle ages, and the aveage of them is \(\displaystyle 26\). So, our median is \(\displaystyle 26\).

Example Question #85 : How To Find Median

What is the median of \(\displaystyle 5,8,10,3,12\)?

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 3\)

\(\displaystyle 10\)

\(\displaystyle 5\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 8\)

Explanation:

In order to find the median of a set of numbers, we must find identify the middle number of the set when all of the set's numbers are arranged in ascending or descending order. Given \(\displaystyle 5,8,10,3,12\) we know that the ordered set is \(\displaystyle 3,5,8,10,12\) and the median is therefore \(\displaystyle 8\).

Example Question #86 : How To Find Median

What is the median of \(\displaystyle -3,7,-7,10,9\)?

Possible Answers:

\(\displaystyle -7\)

\(\displaystyle 7\)

\(\displaystyle 9\)

\(\displaystyle -3\)

\(\displaystyle 10\)

Correct answer:

\(\displaystyle 7\)

Explanation:

In order to find the median of a set of numbers, we must find identify the middle number of the set when all of the set's numbers are arranged in ascending or descending order. Given \(\displaystyle -3,7,-7,10,9\) we know that the ordered set is \(\displaystyle -7,-3,7,9,10\) and the median is therefore \(\displaystyle 7\).

Example Question #87 : How To Find Median

What is the median of \(\displaystyle 2,4,7,8\)?

Possible Answers:

\(\displaystyle \frac{11}2{}\)

\(\displaystyle 4\)

\(\displaystyle \frac{13}{2}\)

\(\displaystyle 7\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle \frac{11}2{}\)

Explanation:

In order to find the median of a set of numbers, we must find identify the middle number of the set when all of the set's numbers are arranged in ascending or descending order. Given \(\displaystyle 2,4,7,8\), we already know that the set is in order, but we have an even number of terms so no specific middle term sticks out.

We'll therefore need to average the two middle terms, \(\displaystyle 4\) and \(\displaystyle 7\), to find this set's median:

\(\displaystyle \frac{4+7}{2}=\frac{11}{2}\).

Example Question #88 : How To Find Median

Gregory is a very inconsistent bowler. In the 10 frames he bowled he knocked down, \(\displaystyle 9,4,10,1,0,8,2,10,4,\) and \(\displaystyle 8\) pins. Gregory just learned how to find median and would like to find the median number of the pins he knocked down, what is the median?

 

 

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 6\)

\(\displaystyle 10\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 6\)

Explanation:

To find the median you must first arrange the numbers from smallest to largest.

\(\displaystyle 0,1,2,4,4,8,8,9,10,10\)

Then you need to get to the middle number which turns out to be

\(\displaystyle 4\)  and  \(\displaystyle 8\)

To find what the median is of this you must find the average of the two numbers:

\(\displaystyle \frac{(4+8)}{2}=6\)

Therefore \(\displaystyle 6\) is your median.

Example Question #81 : How To Find Median

Find the median.

\(\displaystyle 2, 7, 9, 11, 16, 24, 35\)

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 13.5\)

\(\displaystyle 16\)

\(\displaystyle 12\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 11\)

Explanation:

Median is the middle number in the set. There are seven numbers in the set. So, if we cross out a number on each end, we will only have \(\displaystyle 11\) remaining. This is our answer. 

Example Question #90 : How To Find Median

Find the median.

\(\displaystyle 4, 2, 18, 46, 45, 32\)

Possible Answers:

\(\displaystyle 46\)

\(\displaystyle 32\)

\(\displaystyle 18\)

\(\displaystyle 27\)

\(\displaystyle 25\)

Correct answer:

\(\displaystyle 25\)

Explanation:

When finding median, we first arrange from smallest to largest. We now have \(\displaystyle 2, 4, 18, 32, 45, 46\). Since we have six numbers in the set, we will cross out a number on each end. We only are left with \(\displaystyle 18, 32\). When having even amount of numbers in the set, we just take the average of the two numbers.

\(\displaystyle \frac{18+32}{2}=\frac{50}{2}=25\)

Learning Tools by Varsity Tutors