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$Based on the following calculator output, determine the inter-quartile range of the dataset. {:[" 1-Var-Stats "],[ bar(x)=221.857142857],[Sigma x=1553],[Sigmax^(2)=356195],[Sx=44.0659678642],[sigma x=40.7971587646],[n=7],[minX=167],[Q_(1)=176],[Med^(2)=232],[Q_(3)=254],[maxX=285]:} Answer:$

Based on the following calculator output, determine the inter-quartile range of the dataset. $\newline$ $\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=221.857142857 \\ \Sigma x=1553 \\ \Sigma x^{2}=356195 \\ S x=44.0659678642 \\ \sigma x=40.7971587646 \\ n=7 \\ \operatorname{minX}=167 \\ \mathrm{Q}_{1}=176 \\ \mathrm{Med}^{2}=232 \\ \mathrm{Q}_{3}=254 \\ \operatorname{maxX}=285 \end{array}$ $\newline$ Answer:

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Q. Based on the following calculator output, determine the inter-quartile range of the dataset.

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\begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=221.857142857 \\ \Sigma x=1553 \\ \Sigma x^{2}=356195 \\ S x=44.0659678642 \\ \sigma x=40.7971587646 \\ n=7 \\ \operatorname{minX}=167 \\ \mathrm{Q}_{1}=176 \\ \mathrm{Med}^{2}=232 \\ \mathrm{Q}_{3}=254 \\ \operatorname{maxX}=285 \end{array}

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Answer:

Understand IQR Definition: Understand what the inter-quartile range (IQR) is. $\newline$ The inter-quartile range (IQR) is the difference between the third quartile ( $Q_3$ ) and the first quartile ( $Q_1$ ) of a dataset. It measures the spread of the middle $50\%$ of the data.
Identify Quartiles: Identify the first quartile ( $Q_1$ ) and the third quartile ( $Q_3$ ) from the calculator output. $\newline$ According to the given output, the first quartile ( $Q_1$ ) is $176$ and the third quartile ( $Q_3$ ) is $254$ .
Calculate IQR: Calculate the inter-quartile range (IQR) using the values of $Q1$ and $Q3$ . $\newline$ $IQR = Q3 - Q1$ $\newline$ $IQR = 254 - 176$ $\newline$ $IQR = 78$