Question

the data set below has a lower quartile of 13 and an upper quartile of 37. 1, 12, 13, 15, 18, 20, 35, 37, 40, 78 which statement is true about any outliers of the data set? the data set does not have any outliers. the lowest value, 1, is the only outlier. the greatest value, 78, is the only outlier. both 1 and 78 are outliers.

Explanation:

Step1: Calcular rango intercuartílico (IQR)

$IQR = Q_3 - Q_1$
Dado que $Q_1 = 13$ y $Q_3 = 37$, entonces $IQR=37 - 13=24$.

Step2: Calcular límites inferiores y superiores para outliers

Límite inferior para outliers: $Q_1-1.5\times IQR$
$13-1.5\times24=13 - 36=- 23$.
Límite superior para outliers: $Q_3 + 1.5\times IQR$
$37+1.5\times24=37 + 36 = 73$.

Step3: Identificar outliers

El valor 1 es menor que - 23 y el valor 78 es mayor que 73. Entonces, tanto 1 como 78 son outliers.

Answer:

D. Both 1 and 78 are outliers.