The maximum temperatures recorded in Houston for the month of January in 2013 are: 67, 46,...

The maximum temperatures recorded in Houston for the month of January in 2013 are: 67, 46, 56, 50, 47, 60, 57, 64, 67, 69, 73, 75, 72, 45, 42, 52, 63, 62, 68, 69, 71, 71, 75, 79, 79, 78, 77, 81, 77, 61, 67

a. Find Q1, Q2, Q3, the range, and the IQR.

b. Calculate the outlier boundaries for the data set. Are there any outliers?

c. Determine the percentile rank for the 5th order statistic.

Solutions

Expert Solution

Solution:

a. Q1 = 57

Q2 = 67

Q3 = 75

IQR = 18

Explanation

The interquartile range is the difference between the third and first quartiles.

The third quartile is 75.

The first quartile is 57.

The interquartile range = 75 - 57 = 18.

b. outlier boundaries :

Lower Outlier Boundary = 30

Upper Outlier Boundary = 102

Inter-quartile Range (IQR) = Q3 - Q1
Lower Outlier Boundary = Q1 - 1.5 x IQR
Upper Outlier Boundary = Q3 + 1.5 x IQR

c. percentile rank : X = 50, k = 4

Percentile rank = k/n = 4/31 = 0.129 = 12.9%

milcah answered 10 months ago

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