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    IB Math AAHL
    /
    Descriptive Statistics
    /

    Video

    Video Reviews

    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Descriptive Statistics

    Video Reviews

    Watch comprehensive video reviews for Descriptive Statistics, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Data & SamplesMeasuresVisualsRegression

    The video will automatically pause when it reaches a problem.

    Finding variance by hand

    AHL 4.14

    The mathematical definition of variance, which the calculator is using under the hood, is

    σ2=ni=1∑k​fi​(xi​−μ)2​=ni=1∑k​fi​xi2​​−μ2📖


    Here, xi​ are all the existing values in the dataset, and fi​ is the frequency of each value.


    The standard deviation is thus simply the square root of this:

    σ=⎷​ni=1∑k​fi​(xi​−μ)2​​📖



    Example

    Find the variance of the data [2,3,4,4,7].


    First we find that the mean μ=52+3+4+4+7​=4.


    Then

    σ2    ​=ni=1∑k​fi​xi2​​−μ2 =522+32+2⋅42+72​−42 =2.8​

    Finding variance by hand

    AHL 4.14

    The mathematical definition of variance, which the calculator is using under the hood, is

    σ2=ni=1∑k​fi​(xi​−μ)2​=ni=1∑k​fi​xi2​​−μ2📖


    Here, xi​ are all the existing values in the dataset, and fi​ is the frequency of each value.


    The standard deviation is thus simply the square root of this:

    σ=⎷​ni=1∑k​fi​(xi​−μ)2​​📖



    Example

    Find the variance of the data [2,3,4,4,7].


    First we find that the mean μ=52+3+4+4+7​=4.


    Then

    σ2    ​=ni=1∑k​fi​xi2​​−μ2 =522+32+2⋅42+72​−42 =2.8​
    Data & SamplesMeasuresVisualsRegression