Question

1. data set: 4, 8, 6, 2, 9, 7, 5, 7, 8, 10

median = __ upper quartile= lower quartile = __
iqr = ____

Explanation:

Step1: Sort the data set

$2,4,5,6,7,7,8,8,9,10$

Step2: Find the median

There are $n = 10$ data - points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=5$, and the 5th and 6th values are 7 and 7. So, Median $=\frac{7 + 7}{2}=7$.

Step3: Find the lower half

The lower half of the data set is $2,4,5,6,7$.

Step4: Find the lower quartile

There are $n_1 = 5$ data - points in the lower half. The lower quartile $Q_1$ is the $\frac{n_1 + 1}{2}$th value. $\frac{5+1}{2}=3$, so $Q_1 = 5$.

Step5: Find the upper half

The upper half of the data set is $7,8,8,9,10$.

Step6: Find the upper quartile

There are $n_2 = 5$ data - points in the upper half. The upper quartile $Q_3$ is the $\frac{n_2+1}{2}$th value. $\frac{5 + 1}{2}=3$, so $Q_3 = 8$.

Step7: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=8 - 5 = 3$.

Answer:

Median = $7$
Upper Quartile = $8$
Lower Quartile = $5$
IQR = $3$