Question

key question: how do we calculate the interqua inter quartile range formula. outlier formula

Explanation:

Step1: Define quartiles

Quartiles divide a data - set into four equal parts. The first quartile ($Q_1$) is the 25th percentile, the second quartile ($Q_2$) is the 50th percentile (median), and the third quartile ($Q_3$) is the 75th percentile.

Step2: Calculate inter - quartile range (IQR)

The formula for the inter - quartile range is $IQR = Q_3 - Q_1$.

Step3: Define outlier formulas

Lower fence for outliers: $LF=Q_1 - 1.5\times IQR$.
Upper fence for outliers: $UF = Q_3+1.5\times IQR$. Data points less than $LF$ or greater than $UF$ are considered outliers.

Answer:

Inter - quartile range formula: $IQR = Q_3 - Q_1$; Outlier formulas: Lower fence $LF = Q_1 - 1.5\times IQR$, Upper fence $UF=Q_3 + 1.5\times IQR$