Explicit instruction on mean, median, and spread with café examples
When Sarah asks "What's a typical weekend?" she needs more than a gut feeling. Statistics gives her three reliable ways to answer that question. Let's walk through each one.
The mean is what most people think of when they hear "average." You add up all the values and divide by how many there are.
Worked Example: Last 5 weekends
Step 1: Add up all the values
$480 + $520 + $495 + $510 + $470 = $2,475
Step 2: Count how many values
5 weekends
Step 3: Divide sum by count
$2,475 ÷ 5 = $495
The mean of $495 means: if the sales were spread out evenly across all 5 weekends, each weekend would have made $495.
✅ When Mean Works Well
- • Data is roughly symmetric (no extreme outliers)
- • You want to use every data point
- • The data represents a rate or ratio
⚠️ When Mean Gets Distorted
- • One extreme value pulls the average up or down
- • Data is highly skewed
- • You have outliers (like that $2,100 weekend!)
The median is the value exactly in the middle when you sort all values from smallest to largest. Half the data is above it, half is below it.
Worked Example: Same 5 weekends
Step 1: Sort the values from smallest to largest
$470, $480, $495, $510, $520
Step 2: Find the middle position
5 values → middle is position 3
Step 3: Read the middle value
$470, $480, $495, $510, $520
Median = $495
The median tells us: half the weekends made less than $495, and half made more. It's not affected by one extreme value.
What if there's an even number of values?
6 weekends: $480, $520, $495, $510, $470, $460
Sort: $460, $470, $480, $495, $510, $520
With 6 values, there are two middle positions (3 and 4). Take their average:
($480 + $495) ÷ 2 = $487.50
Knowing the "typical" value isn't enough. Sarah also needs to know how consistent the data is. Is sales pretty much the same every weekend, or does it jump around wildly?
Two cafés, same average, very different
Café A (Low Spread)
Weekends: $490, $500, $495, $505, $510
Mean: $500 | Range: $20
Predictable! Can plan inventory closely.
Café B (High Spread)
Weekends: $200, $300, $500, $700, $900
Mean: $500 | Range: $700
Wild variation! Harder to plan inventory.
Range
Maximum - Minimum
Quick measure of spread. Tells you the full span, but sensitive to outliers.
Interpreting Spread
Low spread = values cluster near center, easier to predict
High spread = values scatter widely, harder to forecast
| Measure | What It Tells You | Best When... |
|---|---|---|
| Mean | Balancing point of all data | Data is symmetric, no outliers |
| Median | True middle value | Data has outliers or is skewed |
| Range | Full span from min to max | Quick check, no outliers |
Now Sarah can answer her "What's normal?" question with real statistics:
- Mean: $495 (but remember that $2,100 outlier!)
- Median: $495 (same as mean here—coincidence?)
- Range: $1,715 (from $445 to $2,160)
The median and mean being equal is a clue—the outlier might be pulling the mean up. In the next lesson, we'll learn what to do when a value seems "wrong."