Question

find the 5 number summary for the data shown below.
5 number summary:
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question 37
the boxplot below shows salaries for actuaries and cpas.
latasha makes the first quartile salary for an actuary. aaron makes the third quartile salary for a cpa.
who makes more money?
aaron
latasha
how much more? $
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Explanation:

Step 1: Order the data

First, we order the data set \(5,8,22,33,48,60,66,68,79,84\).

Step 2: Find the minimum

The minimum value is the first value in the ordered list, which is \(5\).

Step 3: Find the first quartile (\(Q_1\))

For a data set with \(n = 10\) values, the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{10+ 1}{4}=2.75\).
Using linear interpolation: \(Q_1=8+(22 - 8)\times0.75=8 + 10.5=18.5\).

Step 4: Find the median (\(Q_2\))

The position of the median for \(n = 10\) is \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\).
\(Q_2=\frac{48 + 60}{2}=54\).

Step 5: Find the third quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25\).
Using linear interpolation: \(Q_3=68+(79 - 68)\times0.25=68+2.75 = 70.75\).

Step 6: Find the maximum

The maximum value is the last value in the ordered list, which is \(84\).

From the box - plot:

• For Actuaries, the first quartile (\(Q_1\)) (Latasha's salary) is approximately \(50\) (in thousands of dollars).
• For CPAs, the third quartile (\(Q_3\)) (Aaron's salary) is approximately \(75\) (in thousands of dollars).

Answer:

\(5,18.5,54,70.75,84\)

For the box - plot question: