Questions: For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, Part 1 of 4 (a) Find the first and third quartiles. The first quartile is The third quartile is

For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, Part 1 of 4 (a) Find the first and third quartiles. The first quartile is The third quartile is
Transcript text: For the data set \begin{tabular}{llllllllllll} \hline 3 & 6 & 4 & 13 & 3 & 7 & 5 & 13 & 3 & 7 & 5 & 15 \\ 3 & 8 & 5 & 27 & 4 & 8 & 6 & 6 & 4 & 11 & & \\ \hline \end{tabular} Part 1 of 4 (a) Find the first and third quartiles. The first quartile is $\square$ The third quartile is $\square$
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Solution

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Solution Steps

Step 1: Sort the Data

The sorted data is: [3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27]

Step 2: Calculate Quartile Positions

The position for the first quartile (Q1) is calculated as \(\frac{1}{4}(n+1)\) = 5.75 The position for the third quartile (Q3) is calculated as \(\frac{3}{4}(n+1)\) = 17.25

Step 3: Interpolation (if necessary)

Since the position for Q1 is not an integer, we interpolate to find Q1 = 4 Since the position for Q3 is not an integer, we interpolate to find Q3 = 8.75

Final Answer:

The first quartile (Q1) is 4 and the third quartile (Q3) is 8.75.

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