Question

common core algebra i b-cr
2
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: Calculate IQR

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

Step2: Find lower outlier threshold

$\text{Lower Threshold} = Q_1 - 1.5 \times IQR = 13 - 1.5 \times 24 = 13 - 36 = -23$

Step3: Find upper outlier threshold

$\text{Upper Threshold} = Q_3 + 1.5 \times IQR = 37 + 1.5 \times 24 = 37 + 36 = 73$

Step4: Check values against thresholds

All values except 78 are between -23 and 73. 78 > 73, so it is an outlier; 1 > -23, so it is not an outlier.

Answer:

The greatest value, 78, is the only outlier.