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Based on the following calculator output, determine the inter-quartile range of the dataset. {:[" 1-Var-Stats "],[ bar(x)=198.571428571],[Sigma x=1390],[Sigmax^(2)=280364],[Sx=26.9249397576],[sigma x=24.9276504128],[n=7],[minX=159],[Q_(1)=175],[Med^(2)=199],[Q_(3)=209],[maxX=244]:} Answer:

Based on the following calculator output, determine the inter-quartile range of the dataset.\newline 1-Var-Stats xˉ=198.571428571Σx=1390Σx2=280364Sx=26.9249397576σx=24.9276504128n=7min⁡X=159Q1=175Med2=199Q3=209max⁡X=244 \begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=198.571428571 \\ \Sigma x=1390 \\ \Sigma x^{2}=280364 \\ S x=26.9249397576 \\ \sigma x=24.9276504128 \\ n=7 \\ \min \mathrm{X}=159 \\ \mathrm{Q}_{1}=175 \\ \mathrm{Med}^{2}=199 \\ \mathrm{Q}_{3}=209 \\ \max \mathrm{X}=244 \end{array} \newlineAnswer:

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Q. Based on the following calculator output, determine the inter-quartile range of the dataset.\newline 1-Var-Stats xˉ=198.571428571Σx=1390Σx2=280364Sx=26.9249397576σx=24.9276504128n=7min⁡X=159Q1=175Med2=199Q3=209max⁡X=244 \begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=198.571428571 \\ \Sigma x=1390 \\ \Sigma x^{2}=280364 \\ S x=26.9249397576 \\ \sigma x=24.9276504128 \\ n=7 \\ \min \mathrm{X}=159 \\ \mathrm{Q}_{1}=175 \\ \mathrm{Med}^{2}=199 \\ \mathrm{Q}_{3}=209 \\ \max \mathrm{X}=244 \end{array} \newlineAnswer:
  1. Understand IQR definition: Understand what the inter-quartile range (IQR) is.\newlineThe inter-quartile range 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 Q11 and Q33: Identify the first quartile (Q1Q_1) and the third quartile (Q3Q_3) from the calculator output.\newlineAccording to the calculator output, Q1Q_1 is 175175 and Q3Q_3 is 209209.
  3. Calculate IQR: Calculate the inter-quartile range (IQR) using the values of Q1Q_1 and Q3Q_3.IQR=Q3−Q1\text{IQR} = Q_3 - Q_1IQR=209−175\text{IQR} = 209 - 175IQR=34\text{IQR} = 34
  4. Verify values and subtraction: Verify that the values used are correct and that the subtraction is done correctly.\newlineThe values for Q1Q1 and Q3Q3 are taken directly from the calculator output, and the subtraction is straightforward. There is no indication of a math error.

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