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)

$IQR = Q_3 - Q_1$
$IQR=37 - 13=24$

Step2: Calcular límites inferiores y superiores para outliers

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

Step3: Identificar outliers

El valor 1 está dentro de los límites (-23 y 73). El valor 78 está por encima del límite superior de 73, por lo que 78 es el único outlier.

Answer:

C. The greatest value, 78, is the only outlier.