Question

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

minimum :
maximum:
q₁ :
q₂ :
q₃ :

1. 67, 100, 94, 77, 80, 62, 79, 68, 95, 86, 73, 84

minimum :
maximum:
q₁ :
q₂ :
q₃ :
(number lines with scales 0–40, 40–80, 60–100 are present)

Explanation:

Problem 2:

Step1: Order the data

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

Step2: Find Minimum and Maximum

The minimum value is the smallest number, which is \( 42 \). The maximum value is the largest number, which is \( 72 \).

Step3: Find Quartiles

The data set has \( n = 9 \) values. The position of the median (\( Q_2 \)) is \( \frac{n + 1}{2}=\frac{9+ 1}{2}=5 \)th value. So \( Q_2 = 58 \).
For \( Q_1 \) (lower quartile), we consider the data below the median: \( 42, 44, 46, 51 \). The position of \( Q_1 \) is \( \frac{4 + 1}{2}=2.5 \)th value. We take the average of the 2nd and 3rd values: \( \frac{44 + 46}{2}=45 \)
For \( Q_3 \) (upper quartile), we consider the data above the median: \( 60, 67, 69, 72 \). The position of \( Q_3 \) is \( \frac{4+ 1}{2}=2.5 \)th value. We take the average of the 2nd and 3rd values: \( \frac{67+ 69}{2}=68 \)

Step1: Order the data

First, we order the data set \( 67, 100, 94, 77, 80, 62, 79, 68, 95, 86, 73, 84 \) from smallest to largest: \( 62, 67, 68, 73, 77, 79, 80, 84, 86, 94, 95, 100 \)

Step2: Find Minimum and Maximum

The minimum value is the smallest number, which is \( 62 \). The maximum value is the largest number, which is \( 100 \).

Step3: Find Quartiles

The data set has \( n = 12 \) values. The position of the median (\( Q_2 \)) is the average of the 6th and 7th values. The 6th value is \( 79 \) and the 7th value is \( 80 \), so \( Q_2=\frac{79 + 80}{2}=79.5 \)
For \( Q_1 \) (lower quartile), we consider the first 6 values: \( 62, 67, 68, 73, 77, 79 \). The position of \( Q_1 \) is the average of the 3rd and 4th values. The 3rd value is \( 68 \) and the 4th value is \( 73 \), so \( Q_1=\frac{68+73}{2}=70.5 \)
For \( Q_3 \) (upper quartile), we consider the last 6 values: \( 80, 84, 86, 94, 95, 100 \). The position of \( Q_3 \) is the average of the 3rd and 4th values. The 3rd value is \( 86 \) and the 4th value is \( 94 \), so \( Q_3=\frac{86 + 94}{2}=90 \)

Answer:

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

Problem 3: