Mean, median, and mode: Computations

All three measures of center on one data set. Sort once at the start — that sorted list serves the median and helps you spot the mode at a glance. Mean is independent of sort order but easier to double-check after.

01 Worked Example Video

Every step of Mean, median, and mode: Computations 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.

Dementia testing (animals)

Numbers of animals listed in one minute by 10 adults:

11, 17, 12, 21, 10, 24, 23, 20, 10, 14

What’s the mean? Round to one decimal place.

mean =

Typing speeds

Typing test results (words per minute) for 10 employees:

45, 52, 38, 60, 47, 52, 41, 55, 50, 52

What’s the mean? Round to one decimal place.

mean =

Book pages read

Pages read this week by 10 members:

120, 95, 140, 85, 95, 130, 110, 95, 105, 125

What’s the mean? Type just the number.

mean =

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

median = middle of sorted list mean = sum ÷ n

mode = most frequent value sort once at the start — helps all three

Three measures of center, one data set. Sort once at the start — that sorted list serves the median directly and helps you spot the mode at a glance. The mean is independent of sort order but easier to double-check on the sorted list. See it live: [3, 6, 5, 6, 4, 8, 6, 2] → the Visualizer surfaces all three measures at once →

Common slips

(1) Mixed up which is which. Median = middle. Mean = average. Mode = most frequent. Verify you answered the part that was asked. (2) Forgot to round. ALEKS often asks for one decimal place — 51.6, not 51.6284. (3) Divided by (n − 1). The mean divides by n, not n − 1. (That’s the sample standard deviation, a different move.)

04 Practice — Step by Step

Practice this problem step by step

Data: 3, 6, 5, 6, 4, 8, 6, 2. Find the median, mean, and mode.

Step 1

Median

Sorted: 2, 3, 4, 5, 6, 6, 6, 8. n = 8 (even), so average the two middle values. What’s the median?

median =

Step 2

Mean

Sum of all 8 values: 3 + 6 + 5 + 6 + 4 + 8 + 6 + 2 = 40. Divide by n = 8 to get the mean.

mean =

Step 3

Mode

In the sorted list, 6 appears three times. Every other value appears once. What’s the mode?

mode =

Q26 Q28

Mean, median, and mode: Computations

You computed all three measures of center.