Statistics

Learn about mean, median, mode, range, data interpretation, and more with clear explanations, examples, and interactive graphs.

Simplified Quantitative Formulas: Statistics

Mean (Average): Mean = (Sum of values) / (Number of values)
Median: Middle value when data is ordered. If even number, median = average of two middle values.
Mode: Most frequently occurring value.
Range: Largest value – smallest value.
Variance: Variance = Σ(x – mean)² / n
Standard Deviation (SD): SD = √Variance
Quartiles & Percentiles: Divide data into quarters/hundredths.
Skewness: Measure of asymmetry of distribution.
Correlation: Measure of relationship between two variables.
Regression: Line/curve that best fits data points.
Variable Definitions: x = value, n = number of values, Σ = sum, SD = standard deviation.

What do these mean? (Super Simple Explanations & Examples)

Mean: 2, 4, 6: Mean = (2+4+6)/3 = 4.
Median: 2, 4, 6: Median = 4. 2, 4, 6, 8: Median = (4+6)/2 = 5.
Mode: 2, 2, 3, 4: Mode = 2.
Range: 2, 4, 6: Range = 6 – 2 = 4.
Variance: 2, 4, 6: Mean = 4, Variance = [(2–4)² + (4–4)² + (6–4)²]/3 = (4+0+4)/3 = 2.67.
Standard Deviation: SD = √2.67 ≈ 1.63.
Quartiles: 1st quartile = 25th percentile, 2nd = median, 3rd = 75th percentile.
Correlation: If height and weight increase together, correlation is positive.
Regression: Fitting a line to data points to predict values.
Variable Definitions: x = value, n = number of values, Σ = sum, SD = standard deviation.

Central Tendency

Central tendency is about finding the center or middle of a set of numbers. The three main types are mean (average), median (middle value), and mode (most common value).

Mean, Median, Mode

Mean: Add all numbers and divide by how many there are.
Median: The middle value when numbers are in order.
Mode: The number that appears most often.

Example

Find the mean, median, and mode of: 2, 4, 4, 6, 8

Solution:

Mean: (2+4+4+6+8) ÷ 5 = 24 ÷ 5 = 4.8
Median: Middle value is 4
Mode: 4 appears most often

Range

The range is the difference between the biggest and smallest numbers in a set. It shows how spread out the numbers are.

Formula

Range = Largest value - Smallest value

Example

Find the range of: 3, 7, 10, 15, 20

Solution:

Largest = 20, Smallest = 3
Range = 20 - 3 = 17

Data Interpretation

Data interpretation means reading and understanding information from tables, charts, and graphs.

Bar Graph Example

Pie Chart Example

Probability & Statistics

Probability is about how likely something is to happen. In statistics, we use probability to make predictions and understand data.

Distributions

Distributions show how data is spread out. The normal distribution is a bell-shaped curve, and the binomial distribution is for things with two outcomes (like flipping a coin).

Regression

Regression is about finding a line or curve that best fits a set of data points. It helps us make predictions.

Practice Questions

Test your understanding of Statistics with 20 fully solved, step-by-step questions designed for beginners.

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