Question

question #3 for a set of data, the lower quartile is 19, the median is 31, and the upper quartile is 48. which value would be an outlier using 1.5×iqr criteria? a -13 b 12 c 75 d 95

Explanation:

Step1: Calculate the inter - quartile range (IQR).

$IQR = Q_3 - Q_1$, where $Q_1 = 19$ and $Q_3=48$. So, $IQR=48 - 19=29$.

Step2: Calculate the lower and upper bounds for non - outliers.

The lower bound is $Q_1-1.5\times IQR=19 - 1.5\times29=19 - 43.5=-24.5$.
The upper bound is $Q_3 + 1.5\times IQR=48+1.5\times29=48 + 43.5 = 91.5$.

Step3: Check each option.

• Option A: $-13>-24.5$, not an outlier.
• Option B: $12>-24.5$, not an outlier.
• Option C: $75<91.5$, not an outlier.
• Option D: $95>91.5$, is an outlier.

Answer:

D. 95