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
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. There are (n = 21) data points.
Step2: Calculate position of first - quartile
The formula to find the position of the first quartile ((Q_1)) is (L_{Q_1}=\frac{n + 1}{4}). Substitute (n = 21) into the formula: (L_{Q_1}=\frac{21+1}{4}=\frac{22}{4}=5.5).
Step3: Interpolate to find (Q_1)
Since the position is 5.5, (Q_1) is the value halfway between 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