median

Mean (average)
Sum of all scores divided by number of scores.
Example: (6 + 8 + 10) / 3 = 8.

Median
Middle score when data are ordered.
Example: For [5, 7, 8], median = 7.

Mode
Most frequent score.
Example: For [2, 3, 3, 5], mode = 3.

Variance (s²)
Average squared deviation from the mean.

Standard Deviation (s)
Square root of variance. Spread of scores around the mean.

Standard Error of the Mean (SEM)
How much sample means vary.
Formula: $$SEM = \frac{s}{\sqrt{n}}$$

t-test
Compares two means.

ANOVA (F-test)
Compares three or more means.

Post Hoc Test
Used after ANOVA to find which groups differ.

Correlation (r)
Strength and direction of a linear relationship. Range: –1 to +1.

Regression
Equation that predicts Y from X.
Example: $$\hat{Y} = a + bX$$

Chi-square (χ²)
Test for categorical data (counts).

Degrees of Freedom (df)
Independent pieces of information in a test.

p-value
Probability of getting the observed result (or more extreme) if the null hypothesis is true.

📱 QR: Interactive glossary (search symbols, formulas, definitions)

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When we look at a set of numbers, the first question is: What is the typical value?
Statistics gives us three common answers — the mean, the median, and the mode.

Each describes “typical” in a different way.

The Mean

The mean is the arithmetic average — the balance point of the data.

Symbolic formula:
$$\bar{X} = \frac{\sum X}{n}$$

Formula in words:
$$\text{Mean} = \frac{\text{sum of scores}}{\text{number of scores}}$$

Where:

• $$\bar{X}$$ = mean (X bar)
• $$\sum X$$ = sum of all scores
• $$n$$ = number of scores

Example: Scores: 10, 8, 7

$$\bar{X} = \frac{10 + 8 + 7}{3} = \frac{25}{3} = 8.33$$

So the mean is about 8.3.

The Median

The median is the middle value when the numbers are placed in order.

Steps:

1. Arrange the scores from smallest to largest.
2. If there are an odd number of scores, the median is the middle one.
3. If there are an even number of scores, the median is the average of the two middle ones.

Examples:

• Data: 5, 7, 9 → Median = 7
• Data: 4, 6, 10, 12 → Median = (6 + 10)/2 = 8

The Mode

The mode is the most frequent score.

Example: Data: 2, 2, 4, 5, 5, 5, 7 → Mode = 5

Definition

• Mean: arithmetic average; balance point.
• Median: middle score; divides data in half.
• Mode: most frequent score.

Visuals

Figure 2.1 — Mean, Median, Mode compared on a skewed dataset. Histogram with three markers: red line = mean, green line = median, purple line = mode.

Why These Matter

• The mean is sensitive to extreme values.
• The median resists extremes and can better represent a “typical” score.
• The mode is useful for categorical or count data.

Together, the three averages give us a rounded view of what is typical in a dataset.

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