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.\n3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11\nwhat is value of the first quartile?\no 3\no 6\no 8\no 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.\n3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11\nwhat is value of the first quartile?\no 3\no 6\no 8\no 11

Answer

Answer:

B. 6

Explanation:

Step1: Arrange data in order

3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11 (already in order)

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

Step3: Find the value of first - quartile

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