Question

What is the third quartile, Q3, of the following distribution?10, 25, 18, 31, 16, 27, 5, 13, 32, 24, 15, 21, 18, 18, 24, 4, 8, 11, 11, 23A.4B.31C.24D.18E.11

Answer 1

`C.\text{ }24`

Step-by-step explanation

First, we have to order this dataset from least to greatest:

`\begin{gathered} 4,\text{ }5,\text{ }8,\text{ }10,\text{ }11,\text{ }11,\text{ }13,\text{ }15,\text{ }16,\text{ }18, \\ \\ 18,\text{ }18,\text{ }21,\text{ }23,\text{ }24,\text{ }24,\text{ }25,\text{ }27,\text{ }31,\text{ }32 \end{gathered}`

The dataset contains 20 values.

The third quartile, Q3, is the median of the bottom half of the dataset.

Splitting the dataset into two, we see that each half contains 10 data values, as shown in each line above.

We have to find the median of the bottom half. Since there are 10 values in the bottom half, the median will be the average of the two middle values.

The two middle values are 24 and 24. The average is:

`\begin{gathered} (24+24)/(2)=(48)/(2) \\ \\ 24 \end{gathered}`

Therefore, the third quartile, Q3, is 24. The correct answer is option C.