Extended practice with varied data and reduced scaffolding
Now you have the tools. Let's practice making decisions about which measure to use and what the results actually mean for the café's business.
In the real world, data is rarely clean. Let's see what happens when we add one outlier to a typical dataset.
Compare these two scenarios
Weekends 1-7 (no outlier):
$480, $495, $510, $505, $490, $500, $515
Mean = $499.29
Median = $500
Difference: Only $0.71ânearly identical!
Weekends 1-8 (with outlier):
$480, $495, $510, $505, $490, $500, $515, $2,100
Mean = $636.88
Median = $502.50
Difference: $134.38âhuge gap!
What does this mean for the café?
If Sarah uses the mean ($636.88) to plan inventory, she'll expect to sell $637 worth of goods every weekendâexcept NO weekend actually hit that number except the one special event. If she uses the median ($502.50), she gets a number that actually represents what most weekends are like.
Real business data often involves decimals and rounding. How do we handle this in statistics?
Example: Daily traffic counts
125, 143, 132, 156, 128, 147, 139
Mean calculation:
Sum = 1,070
Count = 7
Mean = 1,070 Ă· 7 = 152.857...
Rounded: 153 customers/day
Median calculation:
Sorted: 125, 128, 132, 139, 143, 147, 156
Middle (4th): 139
Median = 139 customers/day
The mean (153) is slightly higher than the median (139). This slight right skew comes from the two higher values (156, 147) pulling the average up. For business planning, Sarah might use the median (139) as her "typical day" but note that most days range from 128-147.
Practice deciding between mean and median based on the data characteristics.
Scenario A: Regular weekdays
Customer counts: 42, 45, 48, 51, 44, 46, 50, 43, 47, 49
Recommendation: Mean works well hereâdata is fairly symmetric, no extreme outliers.
Scenario B: Monthly catering orders
Orders in dollars: $2,500, $3,100, $2,800, $15,000, $2,900, $3,200
Recommendation: Median ($3,000) is betterâthe $15,000 outlier would skew the mean to $4,917.
Scenario C: Hourly tip amounts
Tips per hour ($): 12, 15, 18, 22, 25, 28, 32, 85
Recommendation: Median ($25) is betterâthe $85 tip (likely from a large party) distorts the mean.