Question

data set: 23, 18, 17, 9, 21, 27, 12, 14, 13, 16
put data in order: 9, 12, 13, 14, 17, 18, 21, 23, 27
median =
upper quartile=
lower quartile =
iqr =

Explanation:

Step1: Arrange data in ascending order

$9, 12, 13, 14, 17, 18, 21, 23, 27$

Step2: Find the median

There are 9 data - points. The median is the 5th value. So, median $= 17$.

Step3: Find the lower quartile

The lower half of the data is $9, 12, 13, 14$. The median of the lower half (lower quartile, $Q_1$) is the average of the 2nd and 3rd values. $\frac{12 + 13}{2}=12.5$.

Step4: Find the upper quartile

The upper half of the data is $18, 21, 23, 27$. The median of the upper half (upper quartile, $Q_3$) is the average of the 2nd and 3rd values. $\frac{21+23}{2}=22$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=22 - 12.5 = 9.5$

Answer:

Median $= 17$, Lower Quartile $= 12.5$, Upper Quartile $= 22$, $IQR = 9.5$