Questions: At a grocery store in France, shoppers weigh their produce, print the weight onto a sticker, and put them onto the bag to check out. The following values represent the last 54 weights (in grams) for people purchasing bananas. Use technology to calculate the following. 356, 358.3, 360.8, 371.5, 371.5, 373.6, 377.5, 384.1, 401.9, 408.3, 410.3, 430.7, 433.6, 433.6, 433.6, 436.1, 441.2, 442.2, 448.2, 448.4, 448.9, 452.7, 454.7, 460.2, 460.7, 466.9, 468.5, 468.5, 470.9, 471.6, 471.8, 472.1, 474.4, 474.7, 474.8, 474.9, 475.1, 475.6, 476.1, 476.7, 476.7, 476.7, 477.1, 482.5, 487.4, 487.7, 488.3, 491.7, 492.3, 496.8, 501.5, 501.5, 501.9, 502.6 Find the first quartile for this data set. Q1= Find the third quartile for this data set. Q3=

At a grocery store in France, shoppers weigh their produce, print the weight onto a sticker, and put them onto the bag to check out. The following values represent the last 54 weights (in grams) for people purchasing bananas. Use technology to calculate the following. 356, 358.3, 360.8, 371.5, 371.5, 373.6, 377.5, 384.1, 401.9, 408.3, 410.3, 430.7, 433.6, 433.6, 433.6, 436.1, 441.2, 442.2, 448.2, 448.4, 448.9, 452.7, 454.7, 460.2, 460.7, 466.9, 468.5, 468.5, 470.9, 471.6, 471.8, 472.1, 474.4, 474.7, 474.8, 474.9, 475.1, 475.6, 476.1, 476.7, 476.7, 476.7, 477.1, 482.5, 487.4, 487.7, 488.3, 491.7, 492.3, 496.8, 501.5, 501.5, 501.9, 502.6 Find the first quartile for this data set. Q1= Find the third quartile for this data set. Q3=
Transcript text: At a grocery store in France, shoppers weigh their produce, print the weight onto a sticker, and put them onto the bag to check out. The following values represent the last 54 weights (in grams) for people purchasing bananas. Use technology to calculate the following. \begin{tabular}{|r|r|r|r|r|r|} \hline 356 & 358.3 & 360.8 & 371.5 & 371.5 & 373.6 \\ \hline 377.5 & 384.1 & 401.9 & 408.3 & 410.3 & 430.7 \\ \hline 433.6 & 433.6 & 433.6 & 436.1 & 441.2 & 442.2 \\ \hline 448.2 & 448.4 & 448.9 & 452.7 & 454.7 & 460.2 \\ \hline 460.7 & 466.9 & 468.5 & 468.5 & 470.9 & 471.6 \\ \hline 471.8 & 472.1 & 474.4 & 474.7 & 474.8 & 474.9 \\ \hline 475.1 & 475.6 & 476.1 & 476.7 & 476.7 & 476.7 \\ \hline 477.1 & 482.5 & 487.4 & 487.7 & 488.3 & 491.7 \\ \hline 492.3 & 496.8 & 501.5 & 501.5 & 501.9 & 502.6 \\ \hline \end{tabular} Find the first quartile for this data set. $Q_{1}=$ $\square$ Find the third quartile for this data set. $Q_{3}=$ $\square$
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Solution

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Solution Steps

To find the first quartile (Q1) and the third quartile (Q3) of the given data set, we need to:

  1. Sort the data in ascending order.
  2. Calculate the positions of Q1 and Q3 using the formulae:
    • Q1 position = (N+1)/4
    • Q3 position = 3(N+1)/4
  3. Interpolate if necessary to find the exact values of Q1 and Q3.
Step 1: Sort the Data

First, we sort the given weights in ascending order: \[ \begin{array}{cccccc} 356.0 & 358.3 & 360.8 & 371.5 & 371.5 & 373.6 \\ 377.5 & 384.1 & 401.9 & 408.3 & 410.3 & 430.7 \\ 433.6 & 433.6 & 433.6 & 436.1 & 441.2 & 442.2 \\ 448.2 & 448.4 & 448.9 & 452.7 & 454.7 & 460.2 \\ 460.7 & 466.9 & 468.5 & 468.5 & 470.9 & 471.6 \\ 471.8 & 472.1 & 474.4 & 474.7 & 474.8 & 474.9 \\ 475.1 & 475.6 & 476.1 & 476.7 & 476.7 & 476.7 \\ 477.1 & 482.5 & 487.4 & 487.7 & 488.3 & 491.7 \\ 492.3 & 496.8 & 501.5 & 501.5 & 501.9 & 502.6 \\ \end{array} \]

Step 2: Calculate the First Quartile (Q1)

The first quartile \(Q_1\) is the value at the 25th percentile of the sorted data. For the given data set: \[ Q_1 = 433.6 \]

Step 3: Calculate the Third Quartile (Q3)

The third quartile \(Q_3\) is the value at the 75th percentile of the sorted data. For the given data set: \[ Q_3 = 476.7 \]

Final Answer

\(\boxed{Q_1 = 433.6}\)

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