Question

name:
find the 5 number summary and then make a box plot for each set of data.

1. 15,21,16,15,14,8,16,15,15,17,16,14
2. 100,110,110,120,90,130,90,100,110,110,120,110,90,40,130
3. 1,9,17,12,10,15,14,15,24,16,14

Explanation:

Step1: Sort the data

For the third set of data \(1,8,17,12,10,15,14,15,24,16,14\), sort it in ascending order: \(1,8,10,12,14,14,15,15,16,17,24\)

Step2: Find the minimum

The minimum value (\(Min\)) is the first element of the sorted data. So \(Min = 1\)

Step3: Find \(Q_1\)

The first - quartile (\(Q_1\)): The position of \(Q_1\) is \(\frac{n + 1}{4}\) where \(n=11\). \(\frac{11 + 1}{4}=3\). The third element of the sorted data is \(Q_1 = 10\)

Step4: Find the median (\(Q_2\))

The position of the median (\(Q_2\)) is \(\frac{n + 1}{2}\). \(\frac{11+1}{2}=6\). The sixth element of the sorted data is \(Q_2=14\)

Step5: Find \(Q_3\)

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}\). \(\frac{3\times(11 + 1)}{4}=9\). The ninth element of the sorted data is \(Q_3 = 16\)

Step6: Find the maximum

The maximum value (\(Max\)) is the last element of the sorted data. So \(Max=24\)

Answer:

\(Min = 1\), \(Q_1 = 10\), \(Q_2=14\), \(Q_3 = 16\), \(Max = 24\)