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 Worked Example Video

Every step of Median of a data set explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

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

12 students recorded their morning travel time (minutes):

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

What’s the median?

median =

Weekend study hours

11 students recorded weekend study hours:

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

What’s the median?

median =

Fruit prices

8 fruit prices (dollars):

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

What’s the median price?

median = $

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 The Rule

Sort the data smallest to largest, always

n odd: single middle value n even: average the two middle values

The median is the middle of the sorted list, not the list as given. When the count is odd there’s one middle value; when it’s even, average the two around the center. See it live: [3, 5, 7, 8, 10, 12, 14] in the Center & Spread Visualizer →

Common slips

(1) Skipped the sort. The middle of the unsorted list is almost never the median. Sort first. (2) Forgot to average for even n. With n = 12 there’s no single middle — you have to average positions 6 and 7. (3) Confused median with mean. Two different measures — check which the prompt asks for.

04 Practice — Step by Step

Practice this problem step by step

Two data sets: one with 7 values, one with 6 values. Find the median for each.

Step 1

First move

Before finding the median, what should you do to the data?

Step 2

Odd count: 7 values

Data (already sorted): 3, 5, 7, 8, 10, 12, 14. n = 7 (odd), so the median is the single middle value. What is it?

median =

Step 3

Even count: 6 values

New data (already sorted): 2, 4, 6, 8, 10, 12. n = 6 (even), so average the two middle values: 6 and 8. What is the median?

median =

Topic overview Q2

Median of a data set

You walked both odd- and even-count medians.