Question

question #15
find the upper quartile for the data listed in the table.

country	medals	country	medals
ireland	5	south korea	28
france	34	denmark	9
turkey	5	columbia	8
azerbaijan	10	belarus	12

12
34
18
20

Explanation:

Step1: List the data values

5, 5, 6, 8, 9, 10, 10, 12, 28, 34

Step2: Sort the data in ascending order

5, 5, 6, 8, 9, 10, 10, 12, 28, 34

Step3: Calculate the position of the upper - quartile

There are $n = 10$ data points. The position of the upper - quartile ($Q_3$) is given by $i=\frac{3(n + 1)}{4}$. Substitute $n = 10$ into the formula: $i=\frac{3\times(10 + 1)}{4}=\frac{3\times11}{4}=8.25$.

Step4: Find the upper - quartile value

Since the position is $8.25$, $Q_3$ is $0.25$ of the way between the 8th and 9th ordered data values. The 8th value is 12 and the 9th value is 28. $Q_3=12+(28 - 12)\times0.25=12 + 4=16$. But if we use the method of splitting the data into two halves and then finding the median of the upper half:
Split the data into two halves. The upper half of the data set $\{10, 12, 28, 34\}$. The median of this upper - half data set (with $n = 4$ data points) is the average of the 2nd and 3rd values when ordered. The ordered upper - half is $\{10, 12, 28, 34\}$, and $Q_3=\frac{12 + 28}{2}=20$.

Answer:

20