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

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

Answer:

B. 6

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 $L_{Q_1}=\frac{n + 1}{4}$. Here, $n = 21$. So, $L_{Q_1}=\frac{21+1}{4}=\frac{22}{4}=5.5$.

Step3: Determine the value of $Q_1$

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