a poll asks shoppers at the mall how many cups of water they typically drink in a day. the results of the…
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
Answer
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