Question

the minimum of the data is
the first quartile is
the median of the data is
the third quartile is
the maximum of the data is
weight of female dogs (lb.)
4 0 1 3
5 0 8
6 1 2 3 5
7 8
8
9 7

Explanation:

Step1: Write out the data set

The data set from the stem - and - leaf plot is \(40,41,43,50,58,61,62,63,65,78,97\).

Step2: Find the minimum

The minimum is the smallest value. So the minimum is \(40\).

Step3: Sort the data and find the position of the first quartile

The data in ascending order is \(40,41,43,50,58,61,62,63,65,78,97\). There are \(n = 11\) data points. The position of the first quartile \(Q_1\) is \(i=\frac{n + 1}{4}=\frac{11+ 1}{4}=3\). So \(Q_1 = 43\).

Step4: Find the median

The position of the median for \(n = 11\) (odd number of data points) is \(i=\frac{n + 1}{2}=\frac{11+1}{2}=6\). So the median is \(61\).

Step5: Find the position of the third quartile

The position of the third quartile \(Q_3\) is \(i=\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\). So \(Q_3=65\).

Step6: Find the maximum

The maximum is the largest value, which is \(97\).

Answer:

The minimum of the data is \(40\).
The first quartile is \(43\).
The median of the data is \(61\).
The third quartile is \(65\).
The maximum of the data is \(97\).