Question

find the lower and upper quartiles for the data set.

1. order the data from least to greatest.
2. find the median.
3. find the median of the lower half - lower quartile
4. find the median of the upper half - upper quartile

1 do
a. 15, 83, 75, 12, 19, 74, 21

Explanation:

Step1: Order data

$$12,15,19,21,74,75,83$$

Step2: Find median

There are \(n = 7\) data points. The median is the \(\frac{n + 1}{2}\) -th value. \(\frac{7+1}{2}=4\) -th value. So median \(Q_2=21\).

Step3: Find lower quartile

Lower half: \(12,15,19\). There are \(n = 3\) data points. The median of lower half (lower quartile \(Q_1\)) is the \(\frac{3 + 1}{2}=2\) -nd value. So \(Q_1 = 15\).

Step4: Find upper quartile

Upper half: \(74,75,83\). There are \(n=3\) data points. The median of upper half (upper quartile \(Q_3\)) is the \(\frac{3+1}{2}=2\) -nd value. So \(Q_3 = 75\).

Answer:

Lower quartile \(Q_1 = 15\), upper quartile \(Q_3=75\)