Question

a check of prices charged for single vision eye glasses at 20 optical centers resulted in the following dollar amounts.
180 153 185 171 195 207 141 173 203 161
153 184 198 210 172 170 196 181 195 203
find the 1st quartile and 3rd quartile of the prices
q1 160.25
q3 180.5
q1 160
q3 187
q1 160.25
q3 202.75
q1 160.25
q3 190.38

Explanation:

Step1: Sort the data

First, sort the given data in ascending order:
\(141,153,161,170,171,173,181,185,195,195,196,198,203,203,207,210\)

Step2: Find the first quartile (\(Q_1\))

The formula for the first quartile position is \(Q_1\) position \(=\frac{n + 1}{4}\), where \(n = 20\) (number of data points).
\(Q_1\) position \(=\frac{20+ 1}{4}=5.25\)
\(Q_1=171+(173 - 171)\times0.25=171 + 0.5=171.5\)

Step3: Find the third quartile (\(Q_3\))

The formula for the third quartile position is \(Q_3\) position \(=\frac{3(n + 1)}{4}\)
\(Q_3\) position \(=\frac{3\times(20 + 1)}{4}=15.75\)
\(Q_3=203+(207 - 203)\times0.75=203+3=206\)

Answer:

\(Q_1 = 171.5\), \(Q_3=206\)