Question

ch 2 in january of 2006, a family moved to a tropical climate. for the year that followed, they recorded the number of rainy days that occurred each month. the data contained 14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13, 8. what is the first quartile of this data? 11 10.5 8 10

Explanation:

Step1: Sort the data

$8, 10, 10, 11, 11, 11, 11, 12, 13, 13, 14, 14, 14$

Step2: Calculate the position of the first - quartile

The formula for the position of the first - quartile $Q_1$ is $i=\frac{n + 1}{4}$, where $n = 12$ (the number of data points). So $i=\frac{12+1}{4}=3.25$.

Step3: Find the first - quartile

Since $i = 3.25$, $Q_1$ is the value that is $0.25$ of the way between the 3rd and 4th ordered data values. The 3rd value is $10$ and the 4th value is $11$. $Q_1=10+(11 - 10)\times0.25=10.25$ (using linear interpolation). Another common way is to consider the lower half of the data. The lower half of the data is $8, 10, 10, 11, 11, 11$. The median of this lower - half data (which is the first quartile) is $\frac{10 + 11}{2}=10.5$.

Answer:

$10.5$