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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 1-Var-Stats xˉ=221.857142857Σx=1553Σx2=356195Sx=44.0659678642σx=40.7971587646n=7minX=167Q1=176Med2=232Q3=254maxX=285 \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} \newlineAnswer:

Full solution

Q. Based on the following calculator output, determine the inter-quartile range of the dataset.\newline 1-Var-Stats xˉ=221.857142857Σx=1553Σx2=356195Sx=44.0659678642σx=40.7971587646n=7minX=167Q1=176Med2=232Q3=254maxX=285 \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} \newlineAnswer:
  1. Understand IQR Definition: Understand what the inter-quartile range (IQR) is.\newlineThe inter-quartile range (IQR) is the difference between the third quartile (Q3Q_3) and the first quartile (Q1Q_1) of a dataset. It measures the spread of the middle 50%50\% of the data.
  2. Identify Quartiles: Identify the first quartile (Q1Q_1) and the third quartile (Q3Q_3) from the calculator output.\newlineAccording to the given output, the first quartile (Q1Q_1) is 176176 and the third quartile (Q3Q_3) is 254254.
  3. Calculate IQR: Calculate the inter-quartile range (IQR) using the values of Q1Q1 and Q3Q3.\newlineIQR=Q3Q1IQR = Q3 - Q1\newlineIQR=254176IQR = 254 - 176\newlineIQR=78IQR = 78