Question

a poll asks shoppers at the mall how many cups of water they typically drink in a day. the results of the poll are listed below. 3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11. what is value of the first quartile? 3 6 8 11

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11.

Step2: Calculate position of first - quartile

The formula to find the position of the first - quartile ($Q_1$) for a data set of size $n$ is $i=\frac{1}{4}(n + 1)$. Here, $n = 21$. So, $i=\frac{1}{4}(21 + 1)=\frac{22}{4}=5.5$.

Step3: Find the value of first - quartile

Since $i = 5.5$, $Q_1$ is the average of the 5th and 6th ordered data - values. The 5th value is 6 and the 6th value is 6. So, $Q_1=\frac{6 + 6}{2}=6$.

Answer:

6