How to find median

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ISEE Middle Level Quantitative Reasoning › How to find median

Questions 1 - 10

Use the following data set to answer the question.

Find the median.

Explanation

To find the median of a data set, we will first arrange the numbers in ascending order (from smallest to largest) and then we will locate the number in the center or the middle.

So, given the set

we will arrange them in ascending order. We get

Now, we will locate the number that is in the center or the middle. We can see that it is .

Therefore, the median of the data set is .

On the last day of school, Adam asked each of his classmates how many days of school they missed for the entire school year. He created a stem-and-leaf plot with the information.

0 | 0 0 2 4 5 6 8

1 | 0 0 1 2

2 | 3

4 | 7

What is the median number of school days missed by Adam's classmates?

$\dpi{100} 8$

$\dpi{100} 4$

$\dpi{100} 10$

$\dpi{100} 5$

Explanation

In a stem-and-leaf plot, each number on the right side of the vertical lines is a piece of data. For instance, the "4 | 7" means one student missed 47 days(!) of school. Each number on the left of the line represents the ten's digit, and each number on the right of the line represents the one's digit.

We can find the total number of classmates by counting the numbers on the right side of the vertical lines, which in this case is 13.

The median of a group of data represents the physical middle of the data.

If there is an even number of pieces of data, you take the middle two pieces of data, add them up, and divide by two for the median.

If there is an odd number of pieces of data (such as here), one number represents the median. Since we have 13 pieces of data, the 7th value is the median, because we would have 6 pieces smaller or equal to it, and 6 pieces greater than or equal to it.

The seventh piece of data here is the 8, which is "0 | 8". Since the ten's digit is 0, that means that the median number of days missed is 8.

Find the median in this set of numbers:

Explanation

First, order the numbers from least to greatest:

Then, identify the middle number in the set:

Find the median of this set of numbers:

Explanation

First order the numbers from least to greatest:

Then identify the middle number:

Answer:

Find the median in this set of numbers:

Explanation

First, order the numbers from least to greatest:

Then, identify the middle number:

Answer: The median is 598.

Brandon is training for a marathon. Each day after school he runs for two hours. Over the course of two weeks, he runs the following distances:

$\small 12 mi, 14 mi, 13 mi, 12 mi, 14 mi, 16 mi, 15 mi, 9 mi, 14 mi, 12 mi, 10 mi, 11 mi, 14 mi, 12 mi$

What is the median distance that Brandon runs?

There is no median.

Explanation

In order to find the median, we must first put the data in numerical order from least to greatest:

$\small 9mi,10mi,11mi,12mi,12mi,12mi,12mi,13mi,14mi,14mi,14mi,14mi,15mi,16mi$

Next, we must find the number that is in the middle, but since there are fourteen numbers, there is no number that falls exactly in the center. When this happens, we add the two middle numbers together and divide by two. In this case, our middle numbers are $\small 12$ and $\small 13$ .

$\small \frac{12+13}{2}=12.5$

Brandon's median distance is .

Give the median of the following eight scores:

$\left { 61, 67, 80, 72, 76, 73, 90, 68 \right }$

Explanation

Arrange the scores from least to greatest.

$\left { 61, 67, 68, 72, 73, 76, 80, 90 \right }$

There are an even number (eight) of scores, so the median is the arithmetic mean of the middle two scores, 72 and 73. This makes the median

$\frac{72 + 73}{2} = 72.5$

Use the following data set to answer the question:

Find the median.

Explanation

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

So, given the set

we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get

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

$2, 3, 4, 4, 6, {\color{Red} 6}, 7, 7, 7, 8, 9$

We can see that it is 6.

Therefore, the median of the data set is 6.

Find the median in this set of numbers:

Explanation

First place the numbers in order from least to greatest:

Identify the middle number:

In Jane's previous six basketball games, she made the following number of baskets:

What is the median number of baskets she made?

Explanation

The first step to finding the median is to reorder the number of baskets that Jane scored from smallest to largest. This gives us:

The median number is the number in the middle of the set. Given that there are two middle numbers (4 and 6), the average of these numbers will be the median.

The average of 4 and 6 is:

$\frac{4+6}{2}=5$

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