We are given two sets of numbers. We need to find the five-number summary (minimum, first quartile, median, third quartile, and maximum) for each set.

1. Problem Description

We are given two sets of numbers. We need to find the five-number summary (minimum, first quartile, median, third quartile, and maximum) for each set.

2. Solution Steps

Problem 3:

The given set is {9, 15, 19, 5, 20, 15}.

First, sort the set in ascending order: {5, 9, 15, 15, 19, 20}.

The minimum value is

5. The maximum value is

2

0. The median is the average of the middle two numbers: $(15+15)/2 = 15$.

The first quartile (Q1) is the median of the lower half {5, 9, 15}. Q1 =

9. The third quartile (Q3) is the median of the upper half {15, 19, 20}. Q3 =

1

9.

Problem 4:

The given set is {15, 8, 12, 12, 14, 8, 9}.

First, sort the set in ascending order: {8, 8, 9, 12, 12, 14, 15}.

The minimum value is

8. The maximum value is

1

5. The median is the middle value, which is

1

2. The first quartile (Q1) is the median of the lower half {8, 8, 9}. Q1 =

8. The third quartile (Q3) is the median of the upper half {12, 14, 15}. Q3 =

1

4.

3. Final Answer

Problem 3:

Minimum: 5

Q1: 9

Median: 15

Q3: 19

Maximum: 20

Problem 4:

Minimum: 8

Q1: 8

Median: 12

Q3: 14

Maximum: 15