Problem

Find the 5 number summary for the data shown below.
\begin{tabular}{|l|l|}
\hline 34 & 63 \\
\hline 15 & 65 \\
\hline 59 & 75 \\
\hline 78 & 92 \\
\hline 62 & 69 \\
\hline
\end{tabular}
5 number summary:

Answer

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Answer

So, the 5 number summary is: \(\boxed{15, 59, 64, 75, 92}\).

Steps

Step 1 :First, arrange the data in ascending order. The data given is: 34, 63, 15, 65, 59, 75, 78, 92, 62, 69. When arranged in ascending order, the data becomes: \(\boxed{15, 34, 59, 62, 63, 65, 69, 75, 78, 92}\).

Step 2 :The minimum is the smallest number in the data set. Here, the minimum is \(\boxed{15}\).

Step 3 :The first quartile (Q1) is the median of the first half of the data. Since we have 10 numbers, the first half is the first 5 numbers. The median of 15, 34, 59, 62, 63 is \(\boxed{59}\).

Step 4 :The median (Q2) is the middle number of the data set. Since we have 10 numbers, we take the average of the 5th and 6th numbers. The median is \(\boxed{\frac{63+65}{2} = 64}\).

Step 5 :The third quartile (Q3) is the median of the second half of the data. The second half of our data is the last 5 numbers. The median of 65, 69, 75, 78, 92 is \(\boxed{75}\).

Step 6 :The maximum is the largest number in the data set. Here, the maximum is \(\boxed{92}\).

Step 7 :So, the 5 number summary is: \(\boxed{15, 59, 64, 75, 92}\).

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