5) data set 6, 4, 23, 17, 12, 16, 21, 20\nmedian = ____ upper quartile = ____ lower quartile = ____\niqr =…

Explanation:

Step1: Sort the data set

First, sort the data set (4,6,12,16,17,20,21,23).

Step2: Find the median

There are (n = 8) data - points. The median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered values. (\frac{n}{2}=4) and (\frac{n}{2}+1 = 5). The median (Q_2=\frac{16 + 17}{2}=16.5).

Step3: Find the lower half and lower quartile

The lower half of the data set is (4,6,12,16). Since there are (n_1 = 4) data - points in the lower half, the lower quartile (Q_1) is the average of the (\frac{n_1}{2})th and ((\frac{n_1}{2}+1))th ordered values. (\frac{n_1}{2}=2) and (\frac{n_1}{2}+1 = 3). So (Q_1=\frac{6 + 12}{2}=9).

Step4: Find the upper half and upper quartile

The upper half of the data set is (17,20,21,23). Since there are (n_2 = 4) data - points in the upper half, the upper quartile (Q_3) is the average of the (\frac{n_2}{2})th and ((\frac{n_2}{2}+1))th ordered values. (\frac{n_2}{2}=2) and (\frac{n_2}{2}+1 = 3). So (Q_3=\frac{20+21}{2}=20.5).

Step5: Calculate the inter - quartile range (IQR)

The inter - quartile range (IQR=Q_3 - Q_1). So (IQR = 20.5-9 = 11.5).

Answer:

Median = (16.5) Upper Quartile = (20.5) Lower Quartile = (9) IQR = (11.5)