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 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.

Dementia testing (animals) v1

Adults who are being tested for dementia are asked to perform mental tasks such as listing as many animals as they can in one minute. Here are the numbers of animals listed in one minute by 10 adults:

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

(a) What is the median? (Round to one decimal place.)
(b) What is the mean? (Round to one decimal place.)
(c) How many modes does the data set have, and what are their values?

Typing speeds v2

A typing speed test was given to 10 employees. Their results (in words per minute) are:

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

(a) Find the median.
(b) Find the mean.
(c) Identify the mode(s).

Book pages read v3

A reading group of 10 members recorded the number of pages each member read this week:

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

(a) Find the median.
(b) Find the mean.
(c) Identify the mode(s).

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

mean = (sum of values) / n
median = middle of sorted data
mode = most frequent value(s)

Three measures on the same data set. Sort once, then read all three off.

Sort the data once.

Given: 11, 17, 12, 21, 10, 24, 23, 20, 10, 14. Sorted:

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

n = 10. The sorted list does double duty: median lives in the middle; mode is easy to spot when duplicates are adjacent.

Median: average positions 5 and 6.

With n = 10 (even), the median is the average of the two middle values:

median = (14 + 17) / 2 = 15.5

Mean: sum, then divide.

Add the original values (order doesn't matter for the sum):

sum = 11 + 17 + 12 + 21 + 10 + 24 + 23 + 20 + 10 + 14 = 162 mean = 162 / 10 = 16.2

Mode: look for repeats in the sorted list.

Only 10 repeats (twice); every other value appears once. So there is exactly one mode:

mode = 10

On ALEKS, select "one mode" and enter 10 in the value box.

▸ COMMON SLIPS(1) Mean was 16.20 but written as 16.2. ALEKS accepts either; the prompt says "round to one decimal place," so 16.2 is the canonical form. (2) Selected "zero modes" because the value 10 is small. The number of modes is about frequency, not size. 10 repeats — so one mode, value 10. (3) Median = 16 (averaging 12 and 20 from the unsorted list). Sort first. The two middle values of the sorted list are 14 and 17.

04 Practice — Step by Step

Try the same recipe on the typing-speed data set. Sort once; the rest falls out.

Compute the median.

10 typing scores (wpm): 45, 52, 38, 60, 47, 52, 41, 55, 50, 52. What is the median?

median =

Compute the mean.

Same data set: 45, 52, 38, 60, 47, 52, 41, 55, 50, 52. What is the mean (to one decimal place)?

mean =

Identify the mode.

How many modes does 45, 52, 38, 60, 47, 52, 41, 55, 50, 52 have, and what are their values?

mode =

▸ 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.

Q2 Q4