Median - GED Math

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Question

Find the median of the following set of numbers:

Answer

The median of a set of numbers is the number that is in the middle of the set when the numbers are written in increasing order (from smallest to largest).

When a list of numbers includes an even quantity, like the list in this question, you need to find the mean (average) of the two numbers in the middle.

The steps to find the median of this number set are below:

1. Rewrite the list of numbers so that the numbers are written in increasing order

2. Identify the number(s) in the middle of the set

3. Since there are two numbers in the middle of the set, find the average of the two numbers

$\frac{23+25}{2}=\frac{48}{2}=24$

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Question

Which of the following elements can be added to the data set

$\left { 3, 4,4, 4, 5, 5, 5, 6,6, 7\right }$

so that its median remains unchanged?

I:

II:

III:

Answer

The median of a data set with an even number of elements is the mean of the two elements that are in the middle when the elements are arranged in ascending order, such as this one. The middle elements of this ten-element set are both 5, so this is the median.

The median of a data set with an odd number of elements is the element that is in the middle when the elements are arranged in ascending order.

If 0 is added to the set, it becomes

$\left {0, 3, 4,4, 4, 5, 5, 5, 6,6, 7\right }$ .

If 5 is added, it becomes

$\left { 3, 4,4, 4, 5, 5, 5, 5, 6,6, 7\right }$ .

If 100 is added, it becomes

$\left { 3, 4,4, 4, 5, 5, 5, 6,6, 7, 100\right }$ .

In all cases, the middle element is 5, so the median remains 5. The correct choice is "I, II, and III".

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Question

Given the data set $\left { 0, 5, 5, 5, 5, 10, 15, 20, 25 \right }$ , which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

Answer

The median of a data set with an odd number of elements is the middle value when the set is arranged in ascending order; the middle value of this nine-element set is the fifth value, 5.

The mode of a data set is the most frequently occurring element. Here, only 5 appears multiple times, so it is the mode.

The mean of a data set is the sum of its elements divided by the number of elements, which here is 9:

$\frac{0+5+5+5+5+10+15+20+25}{9}= \frac{90}{9} = 10$

The mean and the mode are equal, but the mean is different. The correct answer is "II and III only".

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Question

Veronica went to the mall and bought several gifts for her sister's birthday. The prices of the items were the following:

$8, $10, $6, $7, $10, $2, $5, $3, $4

What is the medianprice of the gifts?

Answer

To find the median, first reorder the prices in ascending order:

$2, $3, $4, $5, $6, $7, $8, $10, $10

The median is the middle number in a data set.

Here, the middle number in this set of nine prices is the 5th number, which is $6.

$2, $3, $4, $5, $6, $7, $8, $10, $10

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Question

Philip went to a family reunion this weekend and met his extended cousins, whose ages were the following:

10, 21, 7, 8, 19, 20, 8, 15, 17, and 13.

What is the medianage?

Answer

The median is the middlenumber in a data set.

To find the median, rearrange the numbers in ascending order and find the middle number:

Given: 10, 21, 7, 8, 19, 20, 8, 15, 17, 13.

In order: 7, 8, 8, 10, 13, 15, 17, 19, 20, 21.

Since the data set has 10 numbers, which is even, the median is the average of the two middle numbers. The two numbers in the middle of this data set are 13 and 15. Their average, or the number in between them, is 14.

Therefore the median age is 14.

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Question

Use the following data set of test scores to answer the question:

Find the median.

Answer

To find the median score, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set.

So, given the set

we will arrange the numbers in ascending order (from smallest to largest). So, we get

Now, we will find the number in the middle.

$78, 81, 83, {\color{Red} 84}, 88, 93, 95$

We can see that it is 84.

Therefore, the median score of the data set is 84.

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Question

A Science class took an exam. Here are the scores of 9 students:

Find the median score.

Answer

To find the median score, we will first arrange the scores in ascending order. Then, we will find the score in the middle of the set.

So, given the set

we will first arrange them in ascending order (from smallest to largest). So, we get

Now, we will find the score in the middle of the set

$76, 78, 81, 81, {\color{Red} 84}, 86, 88, 92, 93$

we can see that it is 84.

Therefore, the median score is 84.

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Question

A class took a Math exam. Here are the test scores of 11 students.

Find the median.

Answer

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set. So, given the set

we will arrange the numbers in ascending order (from smallest to largest). We get

Now, we will find the number in the middle of the set.

$77, 78, 79, 80, 81, {\color{Red} 82}, 85, 89, 93, 94, 99$

Therefore, the median of the data set is 82.

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Question

Solve for the median:

Answer

Reorder the numbers from least to greatest.

$[0,9,11,15,-1] \rightarrow [ -1,0,9,11,15]$

In an odd set of data, the median is the central number of this data set.

The answer is:

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Question

Identify the median:

Answer

Reorder all the numbers in chronological order.

$[1,5,9,1,5,9,-1,-5] \rightarrow [ -5,-1,1,1,5,5,9,9]$

The median of an even set of numbers is the average of the central two numbers.

$\frac{1+5}{2}=3$

The median is:

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Question

A class took a Math exam. Here are the test scores of 9 students.

Find the median.

Answer

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set. So, given the set

we will arrange the numbers in ascending order (from smallest to largest). We get

Now, we will find the number in the middle of the set.

$76, 76, 80, 81, {\color{Red} 84}, 85, 88, 90, 91$

Therefore, the median of the data set is 84.

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Question

Determine the median of the numbers:

Answer

Reorder the numbers from least to greatest.

$[-5,13,-21,-12] \rightarrow [-21,-12,-5,13]$

The median is the average of the central numbers of an ordered set of numbers.

$\frac{-12+(-5)}{2} = \frac{-17}{2} =- \frac{17}{2}$

The answer is: $- \frac{17}{2}$

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Question

Determine the median:

Answer

Rewrite the data set from least to greatest.

$[5,-6,-7,14] \rightarrow [-7,-6,5,14]$

Average the central two numbers.

$\frac{-6+5}{2} = -\frac{1}{2}$

The answer is: $-\frac{1}{2}$

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Question

Find the median:

Answer

Reorder the numbers in the data set from least to greatest.

$[-9,11,-3,1,0]\rightarrow [-9,-3,0,1,11]$

The median is the central number for an odd set of numbers.

The answer is:

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Question

Identify the median:

Answer

Reorder the numbers from least to greatest.

$[2,8,3,0,-5,-4]\rightarrow [ -5,-4,0,2,3,8]$

For an even number of values in a set of data, the median is the average of the central two numbers.

$\frac{0+2}{2} = 1$

The answer is:

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Question

Give the median of the following test scores:

12, 34, 22, 28, 22, 28, 19, 20, 19, 22, 29, 35, 23

Answer

There are thirteen test scores, an odd number, so the median of the test scores is the score which, after the scores are ordered, appears in the middle. Order the scores from greatest to least:

12, 19, 19, 20, 22, 22, 22, 23, 28, 28, 29, 34, 35

As there are scores, we are seeking out the score that ranks at number

$\frac{N + 1}{2} = \frac{13+1}{2} = 7$

That is, the median is the seventh-highest score. This score can be seen to be 22.

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Question

Give the median of the following test scores:

12, 34, 22, 28, 22, 28, 19, 20, 19, 22, 29, 50, 35, 23

Answer

There are fourteen test scores, an even number, so the median of the test scores is the arithmetic mean of the two scores which, after the scores are ordered, appear in the middle. Order the scores from greatest to least:

12, 19, 19, 20, 22, 22, 22, 23, 28, 28, 29, 34, 35, 50

As there are scores, we are seeking out the score that ranks at number

$\frac{N }{2} = \frac{14}{2} = 7$

from the top, and number 7 from the bottom.

That is, the median is the arithmetic mean of the seventh-highest and seventh-lowest scores. These scores can be seen to be 22 and 23, so the median of the scores is

$M = \frac{22+ 23}{2} = \frac{45}{2} = 22.5$

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Question

Identify the median:

Answer

Reorder the numbers from least to greatest.

$[-2,-2,-9,-9,10,10]\rightarrow [ -9,-9,-2,-2,10,10]$

For an even amount of numbers given, the median is the average of the central two numbers.

$\frac{-2+(-2)}{2} = \frac{-4}{2}$

The answer is:

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Question

Use the following data set of student test scores to answer the question:

Find the median.

Answer

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set.

So, given the data set

we will arrange the numbers in ascending order (from smallest to largest). We get

Now, we will find the number in the center. We get

$81, 85, 88,{\color{Red} 90}, 90, 94, 95$

We can see that it is 90.

Therefore, the median of the data set is 90.

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Question

Use the following data set to answer the question:

Find the median.

Answer

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set.

So, given the data set

we will first arrange the numbers in ascending order (from smallest to largest). So, we get

Now, we will find the number in the middle.

$1, 2, 3, 3, 5, {\color{Red} 5}, 6, 6, 6, 6, 8$

We can see that it is 5.

Therefore, the median of the data set is 5.

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