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, 9, 9, 10, 10, 10, 10, 11\nwhat is value of the first quartile?\no 3\no 6\no 8\no 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, 9, 9, 10, 10, 10, 10, 11. There are $n = 20$ data - points.
Step2: Calculate the position of the first - quartile
The formula for the position of the first - quartile $Q_1$ is $i=\frac{n + 1}{4}$. Substitute $n = 20$ into the formula: $i=\frac{20+1}{4}=\frac{21}{4}=5.25$.
Step3: Interpolate to find $Q_1$
Since $i = 5.25$, the first - quartile is between the 5th and 6th ordered data values. The 5th value is 6 and the 6th value is 6. Using linear interpolation, $Q_1=6+(0.25)\times(6 - 6)=6$.
Answer:
6