Learning Objectives
- Understand the collection and presentation of data
- Learn to construct frequency distribution tables
- Represent data graphically using bar graphs, histograms, and frequency polygons
- Calculate measures of central tendency: mean, median, and mode
Key Concepts
Data and Its Types
Primary data: Data collected by the investigator directly for a specific purpose.
Secondary data: Data collected by someone else and used by the investigator.
Frequency Distribution
Ungrouped frequency distribution: Lists each observation and its frequency.
Grouped frequency distribution: Data is organised into class intervals. Example: 0-10, 10-20, 20-30, etc.
Class mark: (Upper limit + Lower limit) / 2
Class size: Upper limit - Lower limit
Graphical Representation
Bar Graph: Rectangular bars of uniform width with heights proportional to the values. Used for ungrouped or categorical data.
Histogram: Similar to bar graph but for continuous grouped data. Bars are adjacent (no gaps). Width of each bar represents the class interval.
Frequency Polygon: Formed by joining the midpoints (class marks) of the tops of histogram bars with straight lines. Can also be drawn independently using class marks and frequencies.
Measures of Central Tendency
Mean (Average): Sum of all observations divided by the total number of observations.
Mean = (x₁ + x₂ + ... + xₙ) / n = Σxᵢ / n
For frequency distribution: Mean = Σ(fᵢxᵢ) / Σfᵢ
Median: The middle value when data is arranged in ascending or descending order.
If n is odd: Median = ((n+1)/2)th observation
If n is even: Median = average of (n/2)th and ((n/2)+1)th observations
Mode: The observation that occurs most frequently.
A data set can have one mode, more than one mode (bimodal/multimodal), or no mode.
Summary
Statistics involves the collection, organisation, analysis, and interpretation of data. Data can be presented in frequency distribution tables and visualised through bar graphs, histograms, and frequency polygons. The three measures of central tendency — mean, median, and mode — provide different ways to describe the central value of a data set.
Important Terms
- Statistics: The science of collecting, organising, analysing, and interpreting data
- Frequency: The number of times a particular observation occurs
- Class Interval: The range within which data values are grouped
- Mean: The arithmetic average of all observations
- Median: The middle value of an ordered data set
- Mode: The most frequently occurring observation
Quick Revision
- Mean = Sum of observations / Number of observations
- Median = middle value (arrange data in order first)
- Mode = most frequent observation
- Histogram: no gaps between bars, used for continuous grouped data
- Frequency polygon: join midpoints of histogram tops
- Class mark = (Upper limit + Lower limit) / 2