Descriptive statistics help organise, summarise, and visualise data. The main areas include:
Central Tendency – Mean, Median
Dispersion – Range (Mode, min, Variance, Standard Deviation, IQR)
Frequency Distribution – Tables and counts.
Data Visualization – Charts and graphs.
Shape of Distribution – Normality, skewness, and kurtosis.
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Mean (Arithmetic Average) – Sum of all values divided by the number of observations.
Median – The middle value when data is arranged in order (useful for skewed data).
Mode – The most frequently occurring value in a dataset (can be more than one).
Example: In a dataset of exam scores (45, 55, 65, 65, 70, 75, 80), the mean is 65, the median is 65, and the mode is 65.
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Data is skewed (e.g., house prices with extreme high values).
Outliers are present, as the median is not affected by extreme values.
Ordinal data needs summarizing (e.g., survey rankings).
The dataset is small or uneven, making the median more representative.
Summarising discrete data like counts (e.g., hospital visits).
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Symmetrical and not skewed.
Without extreme outliers.
Numerical and continuous (e.g., heights, weights, or test scores).
These describe how spread out the data is:
Range – The difference between the highest and lowest value. Mode and Min
Standard Deviation (SD) – The square root of variance; shows how much values deviate from the mean.
Interquartile Range (IQR) – The range of the middle 50% of data (Q3 - Q1).
Example: If two classes have the same average score but one has a high SD, it means scores in that class are more spread out.
Organizes data into categories to show how often each value occurs:
Tables (e.g., frequency tables) – Show counts or percentages.
Grouped data – Data divided into class intervals (e.g., 0-10, 11-20).
Example: A survey of 100 people might show 40% prefer tea, 35% coffee, and 25% juice.
Used to present data clearly:
Histograms – Show frequency distribution for continuous data.
Bar Charts – Compare categorical data.
Pie Charts – Represent proportions.
Box Plots (Box-and-Whisker Plots) – Show distribution, median, and outliers.
Scatter Plots – Show relationships between two variables.
Example: A box plot of students’ scores can show if there are any outliers (exceptionally high or low scores).
Describes the pattern of data:
Symmetric (Normal) Distribution – Bell-shaped curve, mean ≈ median ≈ mode.
Skewed Distribution –
Right-skewed (positive) → Mean > Median > Mode (e.g., income data).
Left-skewed (negative) → Mean < Median < Mode (e.g., exam scores with many high achievers).
Kurtosis – Describes the "peakedness" of a distribution (flat or sharp peak).
Example: Salary distributions are often right-skewed because a few people earn much higher salaries than the majority.