Question

1. 58, 67, 44, 72, 51, 42, 60, 46, 69

minimum : ____________ maximum : ____________
q₁ : ____________ q₂ : __________ q₃ : ____________
number line from 40 to 80 with ticks at 40, 50, 60, 70, 80

Explanation:

Step1: Order the data

First, we order the given data set: \( 42, 44, 46, 51, 58, 60, 67, 69, 72 \)

Step2: Find Minimum and Maximum

The minimum value is the smallest number in the ordered set, and the maximum is the largest.
Minimum: \( 42 \)
Maximum: \( 72 \)

Step3: Find \( Q_2 \) (Median)

Since there are \( n = 9 \) (odd) data points, the median (\( Q_2 \)) is the middle value (the 5th value in the ordered set).
\( Q_2 = 58 \)

Step4: Find \( Q_1 \) (Lower Quartile)

The lower half of the data (excluding the median) is \( 42, 44, 46, 51 \). The median of this lower half is \( Q_1 \). Since there are 4 values (even), we take the average of the 2nd and 3rd values.
\( Q_1=\frac{44 + 46}{2}=\frac{90}{2} = 45 \)

Step5: Find \( Q_3 \) (Upper Quartile)

The upper half of the data (excluding the median) is \( 60, 67, 69, 72 \). The median of this upper half is \( Q_3 \). Since there are 4 values (even), we take the average of the 2nd and 3rd values.
\( Q_3=\frac{67+ 69}{2}=\frac{136}{2}=68 \)

Answer:

Minimum : \( 42 \)
Maximum : \( 72 \)
\( Q_1 \) : \( 45 \)
\( Q_2 \) : \( 58 \)
\( Q_3 \) : \( 68 \)