\$\$10, 10, 10, 10, 8, 8, 8, 8, 12, 12, 11, y\$\$The twelve numbers displayed represent the ages, in years, the the twelve homes on a certain city block. What is the median age, in years, that the twelve houses on the block?

So, you were trying to it is in a good test taker and practice because that the GRE with PowerPrep online. Buuuut climate you had some questions about the quant section—specifically inquiry 12 of ar 4 of exercise Test 1. Those questions experimentation our understanding of Numerical techniques for explicate Data have the right to be type of tricky, but never fear, juniorg8.com has gained your back!

Survey the Question

Let’s search the difficulty for clues regarding what it will be testing, together this will certainly help change our minds come think around what form of math understanding we’ll usage to deal with this question. Pay attention to any type of words that sound math-specific and also anything special about what the number look like, and mark castle on her paper.

You are watching: The twelve numbers shown represent the ages

So the problem wants to recognize the median that a list of numbers. Median definitely sounds choose a math term. If us think carefully, we’ll remember that the median is the middle number of a perform of numbers. We need to expect the we’ll test our Numerical techniques for explicate Data math ability solving this question.

What execute We Know?

Let’s very closely read through the question and also make a perform of the points that we know.

We have a perform of \$12\$ numbersOne of them is absent (\$y\$)We want to find the mean of the perform of numbers

Develop a Plan

Let’s first refresh ours memories about what the mean is. The course, if we’re feeling confident around finding medians of list of numbers, we can just skip best over this refresher.

Concept Refresher – Median

The typical is the “middle” variety of a perform of numbers. That is the number for which we have the same number of numbers that are better than or less than that number in the list. As an example, the average of this list of three numbers (\$1, 2, and 5\$) is \$2\$, since we have one number greater than \$2\$ and one number less than \$2\$ in that list. There are three actions we’ll use for recognize the mean of a perform of numbers:

Put the number in order from the very least to greatest.Start crossing off 2 numbers in ~ a time: very first the the smallest number and also then the biggest number. Protect against crossing off numbers once we have either one or 2 numbers left.If we have only one number left, the typical is that number. If two numbers are left, the typical is the mean of those 2 numbers.

Median instance 1

Let’s start by finding the average for the complying with list the numbers:

\$\$3, -7, 17, 8, 14\$\$

The first step is to put the numbers in bespeak from least to greatest:

\$\$-7, 3, 8, 14, 17\$\$

To uncover the center number in a list, it renders sense that we would start cutting turn off numbers indigenous the two ends. Then whatever remains is the center number! therefore the second step is to start crossing turn off numbers two at a time: the greatest number and the the very least number. So very first we would certainly cross off the \$-7\$ and \$17\$ from the list.

\$\$-7, 3, 8, 14, 17\$\$\$\$3, 8, 14\$\$

Our perform went from 5 numbers under to 3 numbers. Making part progress! However, us still don’t know what the center number is. Let’s cross turn off the least and also greatest numbers again:

\$\$3, 8, 14\$\$\$\$8\$\$

Ah ha! only one number is left, for this reason that must be the center number. The average of the list of number (\$-7, 3, 8, 14, 17\$) is \$8\$.

Median example 2

That wasn’t for this reason bad. Let’s find the median of another set of numbers: \$(3, -7, 17, 8, 14, 6)\$. First, let’s placed the numbers in order from the very least to greatest.

\$\$-7, 3, 6, 8, 14, 17\$\$

Alright, then let’s discover the center number by crossing off the number at the end.

\$\$-7, 3, 6, 8, 14, 17\$\$\$\$3, 6, 8, 14\$\$

Can’t to speak for certain what the center number is yet, so let’s cross turn off the least and greatest numbers again:

\$\$3, 6, 8, 14\$\$\$\$6, 8\$\$

Only two numbers remaining! Looks together if there is a problem though. If us cross off the greatest and also smallest numbers, climate we’ll have no numbers left! Can’t discover the center of an empty perform of numbers. We’ll just need to settle on taking the typical of the two middle numbers.

\$\$;;;;;;;;;;;;;;;;;;;;;;;Median= Average of 6 and 8\$\$\$\$;;;;;;Median = 6+8/2\$\$\$\$;;Median = 14/2\$\$\$\$Median = 7\$\$

Well that’s good to know. If we have an even variety of numbers, then us can’t overcome the numbers off the list two at a time until we have only one number left. There will always be one even number of numbers left, for this reason we’ll arrangement to take the median of the two middle numbers. Excellent. Looks together if we’ve arisen a technique for united state to find the median, or the middle number in a list of numbers. Let’s update our procedures for finding the median to reflect this. To find the average of a perform of numbers:

Put the numbers in bespeak from least to greatest.Start crossing off 2 numbers in ~ a time: first the the smallest number and also then the biggest number. Stop crossing turn off numbers once we have either one or 2 numbers left.If we have only one number left, the average is that number. If two numbers space left, the mean is the typical of those two numbers.Note: If over there is an odd number of numbers, climate the typical will be the value of the solitary number in the middle. If over there is an even number of numbers, then we’ll need to uncover the mean of the two numbers in the middle.

Now the we’ve refreshed our memory around medians, let’s get back to the problem!

We want to discover the median of a list of twelve numbers. We know that to find a average we should first put the number in order from least to greatest. Then for a list through an even variety of numbers, we store crossing turn off numbers two at a time (the greatest and also least numbers) until only two numbers room left. Let’s start by placing the numbers in bespeak from the very least to greatest:

\$\$8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12\$\$

Um, yet where must we placed the \$y\$? The beginning? Wait, or probably the end? Hmmm…we don’t recognize it’s value, so we can’t really encompass it when ordering the numbers from the very least to greatest. If the number are placed in bespeak from least to greatest, the \$y\$ might be the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, or 12th number. So numerous possibilities! that course, we can find the typical for every twelve possibilities, yet that sounds really time-consuming. Looks together if math-ing out this problem isn’t the most reliable solution, therefore let’s try to discover a logical means to fix this concern instead.

As through all numeric entry questions, us are compelled to type in a number answer. Because we don’t recognize the worth of \$y\$, the can’t it is in the median. Otherwise we would require to form in a numerical worth that us don’t know, i m sorry is impossible! Also, the truth that us can type in an actual number answer type of implies that the worth of \$y\$ doesn’t matter. Over there isn’t a “can’t be determined” alternative for this question. Thus, us should have the ability to put \$y\$ everywhere that we desire in the list, discover the middle number, and also report that together our median. Let’s arbitrarily simply put \$y\$ as the first number, climate cross off the least and also greatest numbers till we only have actually the middle two numbers remaining. Climate we deserve to average them to find the median!

Solve the Question

Crossing turn off the least and greatest numbers, two full numbers in ~ a time, we get:

\$\$y, 8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12\$\$\$\$8, 8, 8, 8, 10, 10, 10, 10, 11, 12\$\$\$\$8, 8, 8, 10, 10, 10, 10, 11\$\$\$\$8, 8, 10, 10, 10, 10\$\$\$\$8, 10, 10, 10\$\$\$\$10, 10\$\$

With just two number remaining, the mean must it is in the mean of these 2 numbers. The median of \$10\$ and also \$10\$ would certainly be…wait for it…\$10\$! so the correct answer is \$10\$.

What Did us Learn

Medians! no so awful to deal with. Just put the number of a perform in order from the very least to greatest, overcome off, in pairs, the largest and smallest number of the list, and also we have our median. Just need come remember to take the median of the two center numbers continuing to be at the end if ours list has an even variety of values.

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