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GRADE 12 – Unit 3: Statistics
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Measures of Absolute Dispersion

 

Absolute dispersion measures indicate the extent to which data values deviate from a central point, such as the mean or median. They help us determine the degree of variability within a dataset.

 

  • Range

The range of a dataset is the difference between the highest and lowest values. It is the simplest measure of dispersion.

Range=LStext{Range} = L – S

Where LL is the largest value, and SS is the smallest value in the dataset.

 

  • Inter-Quartile Range (IQR)

The Inter-Quartile Range (IQR) is the difference between the third quartile (Q3Q_3) and the first quartile (Q1Q_1).

IQR=Q3Q1text{IQR} = Q_3 – Q_1

It is a measure of variability that indicates the spread of the middle 50% of the data.

 

  • Mean Deviation

The mean deviation is the average of the absolute deviations from a central value. It can be calculated about the mean, median, or mode.

1. Mean deviation about the mean (MD(xˉ)MD(bar{x})):

MD(xˉ)=xxˉnMD(bar{x}) = frac{sum |x – bar{x}|}{n}

2. Mean deviation about the median (MD(md)MD(m_d)):

MD(md)=xmdnMD(m_d) = frac{sum |x – m_d|}{n}

3. Mean deviation about the mode (MD(mo)MD(m_o)):

MD(mo)=xmonMD(m_o) = frac{sum |x – m_o|}{n}

  • Quartile Deviation (Q)

The quartile deviation is half the difference between the third quartile (Q3Q_3) and the first quartile (Q1Q_1).

QD=Q3Q12QD = frac{Q_3 – Q_1}{2}

  • Variance and Standard Deviation

Variance (σ2sigma^2) measures the average of the squared deviations from the mean:

σ2=(xxˉ)2nsigma^2 = frac{sum (x – bar{x})^2}{n}

Standard Deviation (σsigma) is the square root of the variance:

σ=(xxˉ)2nsigma = sqrt{frac{sum (x – bar{x})^2}{n}}

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