Question

1. data set: 2, 12, 4, 14, 5, 13, 8, 19, 17, 15

median = ____. upper quartile = _ lower quartile = __
iqr = ______________

Explanation:

Step1: Sort the data set

$2,4,5,8,12,13,14,15,17,19$

Step2: Find the median

Since there are $n = 10$ data - points, the median is the average of the 5th and 6th ordered values. Median$=\frac{12 + 13}{2}=12.5$

Step3: Find the lower half

The lower half of the data set is $2,4,5,8,12$. The median of the lower half (lower quartile, $Q_1$) is the 3rd value, so $Q_1 = 5$

Step4: Find the upper half

The upper half of the data set is $13,14,15,17,19$. The median of the upper half (upper quartile, $Q_3$) is the 3rd value of this half, so $Q_3=15$

Step5: Calculate the IQR

$IQR=Q_3 - Q_1=15 - 5 = 10$

Answer:

Median = $12.5$, Upper Quartile = $15$, Lower Quartile = $5$, IQR = $10$