Question

find the third quartile ( q_3 ) of the list of 24 sorted values shown below.
30 30 31 34 34 34 35 40 44 44 45 45 48 48 50 57 58 58 60 62 64 65 74 74
the third quartile ( q_3 ) is (square). (type an integer or a decimal.)

Explanation:

Answer:

To find the third quartile \( Q_3 \) for a list of \( n = 24 \) sorted values, we first find the position of \( Q_3 \) using the formula:

\[
\text{Position of } Q_3 = \frac{3}{4}(n + 1)
\]

Substituting \( n = 24 \):

\[
\text{Position of } Q_3 = \frac{3}{4}(24 + 1) = \frac{3}{4}(25) = 18.75
\]

This means \( Q_3 \) is the value at the 18.75th position in the sorted list. The sorted list (from the image) is:

\( 30, 30, 31, 34, 34, 34, 35, 40, 44, 44, 45, 45, 48, 48, 50, 57, 58, 58, 60, 62, 64, 65, 74, 74 \)

The 18th value is \( 58 \), and the 19th value is \( 60 \). To find the 18.75th value, we interpolate:

\[
Q_3 = \text{18th value} + 0.75 \times (\text{19th value} - \text{18th value})
\]

\[
Q_3 = 58 + 0.75 \times (60 - 58)
\]

\[
Q_3 = 58 + 0.75 \times 2
\]

\[
Q_3 = 58 + 1.5 = 59.5
\]

\( 59.5 \)