Question

practice 5 (from unit 1, lesson 2)
what is the five - number summary for the data?
2 2 4 4 5 5 6 7 9 18
type the answers in the boxes.

Explanation:

Step1: Find the minimum

The minimum value in the data - set \(2,2,4,4,5,5,6,7,9,18\) is \(2\).

Step2: Find the first quartile (\(Q_1\))

First, find the median of the lower half of the data. The data has \(n = 10\) values. The lower half is \(2,2,4,4,5\). The median of this lower - half (the first quartile) is \(4\).

Step3: Find the median (\(Q_2\))

Since \(n = 10\) (an even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{5 + 5}{2}=5\).

Step4: Find the third quartile (\(Q_3\))

The upper half of the data is \(5,6,7,9,18\). The median of this upper - half (the third quartile) is \(7\).

Step5: Find the maximum

The maximum value in the data - set is \(18\).

Answer:

\(2,4,5,7,18\)