MAT-144 · Mathematical Reasoning Topic 05 · Statistics
Topic 05 · Review · Q6

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.

▸ 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.

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

Two-bar mean v1

The graph below shows two black bars. Adjust the light bar so that it has the mean height of the two black bars.

Visual prompt: ALEKS shows two black bars at heights of, for example, 8 and 4. Drag the light bar's top until it sits at the midpoint of the two black bars.

Two-bar mean — heights 10 and 6 v2

Two black bars are shown at heights 10 and 6. Adjust the light bar so its height equals the mean of the two black bars.

Two-bar mean — heights 7 and 3 v3

Two black bars are shown at heights 7 and 3. Adjust the light bar to the mean height.

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.
mean = (b₁ + b₂) / 2
Two values; mean is their midpoint — exactly halfway between.
1

Read both bar heights.

Say the two black bars sit at heights b₁ = 8 and b₂ = 4 (use the y-axis gridlines to estimate).

2

Compute the mean.

mean = (8 + 4) / 2 = 6

The mean is 6 — exactly halfway between 4 and 8. Visually, the light bar's top should land on the dashed midline.

3

Drag the light bar to that height.

On ALEKS, click and drag the top edge of the light bar until it sits at the computed mean. The tool snaps to gridlines, so reading the y-axis carefully in step 1 makes step 3 trivial.

▸ COMMON SLIPS(1) Picked one of the bar heights. The mean is the average of the two, not either one. It must land between them. (2) Misread a bar height. Look at the y-axis gridline labels carefully — the image isn't always to scale. (3) Used the median formula by accident. With only two values, median and mean are both the midpoint, so this question has no median/mean distinction to worry about.

Practice with two different bar heights. The mean always sits at the midpoint.

1

Compute the mean of two bars.

Two black bars have heights 10 and 6. What height should the light bar be?
mean =
2

Now with smaller bars.

Two black bars have heights 7 and 3. Mean?
mean =
▸ 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.