Question

question #7
find the upper quartile of the following set of data:
1 1 4 6 7
10 13 15 18
o 12
o 15
o 7
o 14

question #8
find the interquartile range and sample standard deviation for the set of data.

o iqr = 7.1 and s = 4.15
o iqr = 11.3 and s = 6.06
o iqr = 5.7 and s = 4.66
iqr = 8.9 and s = 7.03

Explanation:

Step1: Sort the data

The data set is already sorted: \(1,1,4,6,7,10,13,15,18\)

Step2: Find the median

Since \(n = 9\) (odd), the median \(Q_2\) is the \(\frac{n + 1}{2}\)th value. \(\frac{9+1}{2}=5\)th value. So \(Q_2 = 7\)

Step3: Split the data

The upper half of the data is \(10,13,15,18\)

Step4: Find the upper - quartile (\(Q_3\))

Since \(n = 4\) (even) for the upper half, \(Q_3=\frac{13 + 15}{2}=\frac{28}{2}=14\)

Answer:

\(14\)