Question

the five number summary of a dataset was found to be: 45, 51, 60, 65, 70 an observation is considered an outlier if it is below: an observation is considered an outlier if it is above:

Explanation:

Step1: Identify the five - number summary components

The five - number summary is given as \( \text{Minimum}=45 \), \( Q_1 = 51 \), \( \text{Median}=60 \), \( Q_3=65 \), \( \text{Maximum}=70 \)

Step2: Calculate the Inter - Quartile Range (IQR)

The formula for the inter - quartile range is \( IQR=Q_3 - Q_1 \)
Substitute \( Q_3 = 65 \) and \( Q_1=51 \) into the formula:
\( IQR=65 - 51=14 \)

Step3: Calculate the lower bound for outliers

The formula for the lower bound (the value below which a data point is considered an outlier) is \( \text{Lower Bound}=Q_1-1.5\times IQR \)
Substitute \( Q_1 = 51 \) and \( IQR = 14 \) into the formula:
\( \text{Lower Bound}=51-1.5\times14=51 - 21 = 30 \)

Step4: Calculate the upper bound for outliers

The formula for the upper bound (the value above which a data point is considered an outlier) is \( \text{Upper Bound}=Q_3 + 1.5\times IQR \)
Substitute \( Q_3=65 \) and \( IQR = 14 \) into the formula:
\( \text{Upper Bound}=65+1.5\times14=65 + 21=86 \)

Answer:

An observation is considered an outlier if it is below: \( \boldsymbol{30} \)

An observation is considered an outlier if it is above: \( \boldsymbol{86} \)