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 first - value in the sorted list. Minimum = 5.3

Step3: Find the first quartile ($Q_1$)

The position of $Q_1$ is $\frac{n + 1}{4}=\frac{16+1}{4}=4.25$. So, $Q_1$ is the value 0.25 of the way between the 4th and 5th ordered values. The 4th value is 5.8 and the 5th value is 6.0. $Q_1=5.8+(6.0 - 5.8)\times0.25 = 5.85$

Step4: Find the median ($Q_2$)

The position of the median for $n = 16$ (an even - numbered data set) is $\frac{n}{2}=8$ and $\frac{n}{2}+1 = 9$. The median $Q_2=\frac{6.2 + 6.6}{2}=6.4$

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(16 + 1)}{4}=12.75$. So, $Q_3$ is the value 0.75 of the way between the 12th and 13th ordered values. The 12th value is 6.8 and the 13th value is 7.0. $Q_3=6.8+(7.0 - 6.8)\times0.75=6.95$

Step6: Find the maximum

The maximum value is the last value in the sorted list. Maximum = 8.8

Answer:

Minimum	$Q_1$	$Q_2$	$Q_3$	Maximum