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6: Grouping with Z-Scores

Students convert raw scores to z-scores, use z-score thresholds to classify observations into groups, and identify statistical outliers using standard deviation cutoffs.

Z-Scores in Google Sheets

Click to show Z-Scores in Google Sheets example problem

Purpose: Practice calculating Z-scores in Google Sheets using the population mean (μ, mu = 120) and population standard deviation (σ, sigma = 15).
Follow these steps:

  1. Open the Google Sheet Template: Google Sheet Template
  2. File → Make a copy.
  3. Paste the table below into the sheet (two columns: Name and BP).
  4. Use μ = 120 and σ = 15 to compute Z for each BP.
  5. Formula hint: (B2 - μ)/σ. Here B2 means the first BP value in column B. After typing the formula in the first row, place your mouse on the small square in the bottom-right corner of the cell (the fill handle) and drag it down. The spreadsheet will automatically change B2 to B3 for the next row, then B4, and so on, so each patient's BP gets its own Z-score.
  6. Pro Tip: Advanced users can highlight the formula cell and the rows below it, then press ⌘D (Mac) or Ctrl+D (Windows) to autofill the formula quickly.

Patient Name Systolic BP (mmHg)
Berta 78
Cedric 122
Isha 124
Jennifer 119
Pravalika 101
Ravikumar 140
Sthefani 160
Tanitha 111

Question: Which named patient has a Z-score between -2 and -1 standard deviations?

 

Lowest Biodiversity Scores Using Z-Scores

Click to show Lowest Biodiversity Scores Using Z-Scores example problem
Ecologists assess biodiversity across four Chicago-area villages by calculating Z-scores for plant diversity, insect diversity, and bird diversity. Based on the data provided below, which village shows the HIGHEST level of biodiversity overall?
Village Plant
Z-Score		 Insect
Z-Score		 Bird
Z-Score		 Total
Z-Score
Des Plaines 2.11 -0.89 0.33 1.60
Elmhurst -1.34 -0.40 -1.77 -3.50
Highland Park 1.84 0.77 1.40 4.00
Morton Grove -0.05 -2.04 1.19 -0.90