Problem

Given the data set {12, 15, 16, 20, 22, 25, 28, 30, 33, 35}, find the five number summary.

Answer

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Answer

Step 6: Find the maximum. The maximum is the last number in our data set. So, the maximum is \(35\).

Steps

Step 1 :Step 1: Sort the data set in ascending order. The data set is already sorted so we don't need to do anything.

Step 2 :Step 2: Find the minimum. The minimum is the first number in our data set. So, the minimum is \(12\).

Step 3 :Step 3: Find the first quartile, Q1. This is the median of the first half of our data set. Since we have 10 numbers, the first half is {12, 15, 16, 20, 22}. The median of this set is \(16\).

Step 4 :Step 4: Find the median. The median is the middle number of the data set. Since we have 10 numbers, the median is the average of the 5th and 6th numbers. So, the median is \(\frac{22+25}{2} = 23.5\).

Step 5 :Step 5: Find the third quartile, Q3. This is the median of the second half of our data set. The second half is {25, 28, 30, 33, 35}. The median of this set is \(30\).

Step 6 :Step 6: Find the maximum. The maximum is the last number in our data set. So, the maximum is \(35\).

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