Question

find the 5 number summary for the data shown below.
66 79
22 8
84 48
5 33
68 60
5 number summary:
5, , 54, , 84
question help: video 1 video 2 video 3 video 4

Explanation:

Step1: Sort the data

First, we list all the data points: \(5,8,22,33,48,60,66,68,79,84\).

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

The formula for the position of \(Q_1\) is \(\frac{n + 1}{4}\) where \(n=10\) (number of data points). \(\frac{10+1}{4}=2.75\).
Using linear - interpolation: \(Q_1=8+(22 - 8)\times0.75=8 + 14\times0.75=8+10.5 = 18.5\).

Step3: Find the third quartile (\(Q_3\))

The formula for the position of \(Q_3\) is \(\frac{3(n + 1)}{4}\). \(\frac{3\times(10 + 1)}{4}=8.25\).
Using linear - interpolation: \(Q_3=68+(79 - 68)\times0.25=68+11\times0.25=68 + 2.75=70.75\).

Answer:

\(5\), \(18.5\), \(54\), \(70.75\), \(84\)