Question

the weights of 16 randomly selected acorns from california black oak trees are recorded below. 6.7, 8.8, 6.2, 6.8, 5.3, 6.0, 7.2, 6.2, 5.7, 5.7, 6.6, 6.1, 5.8, 6.8, 7.0, 7.2. enter the five - number summary below. do not round any answers in this problem. minimum q1 q2 q3 maximum

Explanation:

Step1: Sort the data

\[5.3, 5.7, 5.7, 5.8, 6.0, 6.1, 6.2, 6.2, 6.6, 6.7, 6.8, 6.8, 7.0, 7.2, 7.2, 8.8\]

Step2: Find the minimum

The minimum value is the smallest number in the sorted - data set. So, the minimum is \(5.3\).

Step3: Find the first quartile \(Q_1\)

Since \(n = 16\), the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{16+1}{4}=4.25\). The first quartile is \(0.75\times5.8 + 0.25\times6.0=5.85\).

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

Since \(n = 16\) (an even - numbered data set), \(Q_2=\frac{6.2 + 6.6}{2}=6.4\).

Step5: Find the third quartile \(Q_3\)

The position of \(Q_3\) is \(3\times\frac{n + 1}{4}=3\times4.25 = 12.75\). So, \(Q_3=0.25\times6.8+0.75\times7.0 = 6.95\).

Step6: Find the maximum

The maximum value is the largest number in the sorted - data set. So, the maximum is \(8.8\).

Answer:

Minimum	\(Q_1\)	\(Q_2\)	\(Q_3\)	Maximum