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Mathematics · Class 10 · Chapter 22: Basic Statistics

8 min

Key points

Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data
Data can be classified as Primary Data (collected directly) and Secondary Data (obtained from other sources)
Measures of Central Tendency include Mean, Median and Mode - these show the central value of data
Arithmetic Mean = Sum of all observations ÷ Number of observations
For grouped data, Mean = Σfx/Σf where f is frequency and x is class mark
Median is the middle value when data is arranged in ascending or descending order
Mode is the value that occurs most frequently in the data set
Range = Highest value - Lowest value, measures the spread of data
Frequency Distribution Table organizes raw data into classes with their frequencies

Definitions

Statistics: Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.
Primary Data: Primary data is the data collected directly by the investigator from the original source for the first time.
Arithmetic Mean: The arithmetic mean of a set of observations is the sum of all observations divided by the number of observations.
Median: The median is the middle value of the observations when they are arranged in ascending or descending order of magnitude.
Mode: The mode is the value which occurs most frequently in a set of observations.

Worked example

Calculate the arithmetic mean of the following data: 15, 18, 12, 20, 16, 14, 19, 13, 17, 11 (4 marks)

The arithmetic mean of the given data is 15.5

Common mistakes

Students often forget to arrange data in order before finding median
Confusing class mark with class interval in grouped data mean calculation
Not writing the formula before solving numerical problems
Mixing up definitions of primary and secondary data
Forgetting to divide by total frequency (Σf) in grouped data mean formula

Quick recap

Statistics is the science of collecting, organizing, presenting, analyzing and interpreting numerical data. Remember the exact textbook definitions of population (complete group), sample (part of population), variable (characteristic that changes), primary data (collected directly) and secondary data (already collected). For calculations, always show complete working with formulas for mean, median, and mode.

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