SSAT Middle Level Quantitative - How to find median

Give the median of the data set:

$\left { 45, 48, 49, 49, 59, 60, 66, 68, 77 \right }$

Explanation

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

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:

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

Shelly took five tests and quizzes this semester in school. If her grades were , , , , and , what is her median test score?

Explanation

First, order the test scores from least to greatest:

Identify the middle test score:

Answer: Shelley's median test score is 92.

What is the median of the following set of numbers:

No number is the median for this set of numbers

Explanation

The median is the number with an equal number of other items both above and below it. There are 9 total numbers in the list, 4 of them are below 7, and 4 of them are above 7.

Subtract the range from the median in this set of numbers:

Explanation

First, order the numbers from least to greatest:

In order to find the range, subtract the smallest number from the greatest:

Now, find the median by identifying the middle number:

Finally, subtract the range from the median:

Given the following data sets of data, identify how the median would change if an additional data point of was added to the new set?

Data Set: $\textup{3, 1, 7, 9, 10, 11}$

New Data Set: $\textup{3, 1, 7, 9, 10, 11, 5}$

$\textup{The median will decrease by 1.}$

$\textup{The median will increase by 1.}$

$\textup{The median will remain unchanged.}$

$\textup{The median will increase by 5.}$

Explanation

First, we need to find the median for the first data set:

We must put the numbers in order from least to greatest:

$\textup{1, 3, 7, 9, 10, 11}$

Since there is an even number of items in the data set, we will take the average of the middle two numbers to find the median.

$\frac{7+9}{2}=8$

The median for this data set is:

$\text{median}=8$

Next, we must find the new median for the new data set:

$\textup{3, 1, 7, 9, 10, 11, 5}$

Again, we must put the numbers in order from least to greatest:

$\textup{1, 3, 5, 7, 9, 10, 11}$

Since there is an odd number of items, we can choose the middle number to be the median.

In this case, the middle number is , which means the new median is:

$\text{median}=7$

Therefore, we know that the median will decrease by .

On a math test that the teacher gave her students, the scores were as follows:

What was the median score?

Explanation

The median is the middle number in a set when the set of numbers is ordered sequentially.

When the intial set is reordered sequentially, you get the bottom set. (The top set is the original ordering of the numbers.)

In this sequential set of 7 numbers, the number 89 is in the fourth posiiton and exactly in the middle. Therefore, it is the mean.

What is the median of the values , , , , ?

Explanation

The median of a set of values is the value that is in the middle when you rearrange the values from least to greatest. In this set, the values can be rearranged as , , , , and the median is .