✅ 1. Percentages

(From Medical Statistics Made Easy, pages 7–8)

What it means

“Percent” means “per 100.”

A percentage tells you how many out of 100 are in a group.

How to calculate

Percentage = (number in the category ÷ total number) × 100

Example from the book

14 patients out of 80 were in the 30–39 age band.

Percentage = (14 ÷ 80) × 100 = 17.5%

Key point

Percentages help compare groups, but they can hide small sample sizes.

✅ 2. Mean (Average)xˉ

(From pages 9–11)

What it means

Mean = total of all values divided by the number of values.

When to use

Use the mean when the data are evenly spread (normal distribution).

Example from the book

Ages: 52, 55, 56, 58, 59

Sum = 280

Mean = 280 ÷ 5 = 56

Warning

A very large or very small value can pull the mean in one direction.

If the data are skewed, use the median instead.

✅ 3. Median

(From pages 12–13)

What it means

The median is the middle value when numbers are arranged from smallest to largest.

When to use

Use the median when the data are skewed or have outliers.

Example from the book

Data: 52, 55, 56, 58, 59 → median is 56

Add a new age 92: data becomes 52, 55, 56, 58, 59, 92

Middle values are 56 and 58 → median is 57

This represents the data better than the mean.

Extra

The median is often reported with the interquartile range (IQR), which shows the middle half of the data.

✅ 4. Mode

(From pages 14–15)

What it means

The mode is the value or category that appears most often.

When to use

Useful for categorical data (like eye colour).

Book example

In a clinic:

Brown eyes = most common → Mode = “brown”

Extra

A distribution can be “bimodal” (two peaks), meaning two common groups exist.

✅ 5. Standard Deviation (SD)

(From pages 16–19)

What it means

Standard deviation describes how spread out the values are around the mean.

When to use

Use SD only when the data are normally distributed.

Key numbers to remember

In a normal (bell-shaped) distribution:

• 68.2% of values lie within 1 standard deviation of the mean
• 95.4% lie within 2 standard deviations
• 99.7% lie within 3 standard deviations

Book example

Mean weight = 80 kg

SD = 5 kg

This means:

• Most people (68%) weigh between 75 and 85 kg

• Almost all (95%) weigh between 70 and 90 kg

• Nearly everyone (99.7%) weighs between 65 and 95 kg

Warning

If the mean minus 2 SD gives an impossible number (like negative days in hospital), the data are not normally distributed, so SD should not be used.

Here is the same standard deviation example, now with x clearly defined inside it.

Example: Standard Deviation (Sample)

Data (observations = x values):

x = 2, 4, 6

Step 1: Find the mean (x̄)

x̄ = (2 + 4 + 6) / 3 = 4

Step 2: Calculate deviations (x − x̄)

Step 3: Square the deviations

Sum of squared deviations = 8

Step 4: Divide by (n − 1)

n = number of x values = 3

Variance = 8 / (3 − 1) = 4

Step 5: Square root

Standard deviation = √4 = 2

Final exam-ready statement:

• x = individual observation
• x̄ = mean of observations
• n = total number of observations
• SD = 2

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