Median of a data set

Sort the data first; the median is the middle value (or the average of the two middle values when n is even). The most common ALEKS slip is skipping the sort and reading off the middle of the unsorted list.

01 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Morning travel times v1

A group of 12 students from the same middle school have been asked to record how much time they spent this morning traveling from home to school. Here are the results (in minutes):

8, 9, 10, 10, 11, 12, 4, 14, 4, 7, 14, 13

Find the median travel time for that group of students.

Weekend study hours v2

A teacher asked 11 students to record how many hours they spent studying over the weekend:

3, 7, 2, 5, 9, 6, 4, 8, 5, 3, 10

Find the median number of study hours.

Fruit prices v3

A grocery shopper records the prices (in dollars) of 8 different fruits she bought this week:

1.20, 0.85, 2.40, 1.50, 1.80, 0.95, 3.10, 1.65

Find the median price.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 How to Solve It

median = middle value of the sorted data
if n is even, average the two middle values

Always sort first. The middle is the middle of the sorted list, not the list as given.

Sort the data from smallest to largest.

Given: 8, 9, 10, 10, 11, 12, 4, 14, 4, 7, 14, 13. Sorted:

4, 4, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14

n = 12, so n is even. The two middle values are in positions 6 and 7.

Average the two middle values.

Positions 6 and 7 are both 10:

median = (10 + 10) / 2 = 10 minutes

When the two middle values happen to be the same, the average is just that value — no calculation needed beyond confirming.

▸ COMMON SLIPS(1) Read the middle of the unsorted list. The 6th value as given is 12. The 6th value when sorted is 10. Always sort first. (2) Forgot to average for even n. With n = 12 there is no single middle — you must average the two middle entries. (3) Used the mean instead. Median and mean are different measures; check which one the prompt asks for.

04 Practice — Step by Step

Try a different data set. Same recipe: sort first, then read the middle.

Sort the data and find the median.

11 students recorded weekend study hours: 3, 7, 2, 5, 9, 6, 4, 8, 5, 3, 10. What is the median?

median =

Now an even-count data set.

8 fruit prices (in dollars): 1.20, 0.85, 2.40, 1.50, 1.80, 0.95, 3.10, 1.65. What is the median?

median = $

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Topic overview Q2