Understanding the mean graphically: Two bars

ALEKS shows two black bars of different heights and asks you to drag a light bar until its height equals their mean. The arithmetic is dead simple — average the two heights — but the picture reinforces the "balance" intuition: the mean sits exactly halfway between two values.

01 Worked Example Video

Every step of Understanding the mean graphically: Two bars 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.

Two-bar mean — heights 8 and 4

Two black bars are shown at heights 8 and 4. What’s the mean height?

mean =

Two-bar mean — heights 10 and 6

Two black bars are shown at heights 10 and 6. What’s the mean height?

mean =

Two-bar mean — heights 7 and 3

Two black bars are shown at heights 7 and 3. What’s the mean height?

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

mean of two values = (a + b) / 2 the exact midpoint between them

Visually, the mean is halfway between two bar tops not weighted by height

For just two values, the mean is the midpoint. Add them, divide by 2. The bar-drag view reinforces the geometric intuition: the mean sits exactly halfway between the two bar heights. See it live: [8, 4] → the mean marker lands at exactly 6 in the Visualizer →

Common slips

(1) Averaged the wrong thing. The mean averages the heights — not the positions on the axis or the widths of the bars. (2) Estimated instead of computing. Dragging by eye lands close, but the exact mean is (a + b) / 2. Compute first, then place. (3) Assumed a whole number. If the two bars are 7 and 4, the mean is 5.5 — not 5 or 6.

04 Practice — Step by Step

Practice this problem step by step

Two black bars sit at heights 8 and 4. Drag the light bar to the mean height.

Step 1

What’s the mean of two values?

For two values a and b, the mean is:

Step 2

Compute the mean

Compute (8 + 4) / 2. Type just the number.

mean =

Step 3

Drag the light bar to the mean height

Drag the top of the middle bar to a height of 6. Grid snaps to half-units on release.

Drag the top of the middle bar to the mean height of A and B.

Q5 Topic overview

Understanding the mean graphically: Two bars

You walked the two-bar mean visually and arithmetically.