Practice creating box-and-whisker plots with given data sets and fill in minimum, maximum, Q1, Q2, and Q3 values.

To solve these problems, we need to find the "Five Number Summary" for each set of data. This includes the Minimum, Maximum, Median (Q2), Lower Quartile (Q1), and Upper Quartile (Q3).

Here is the step-by-step method:
1. Order the numbers: List them from smallest to largest.
2. Find the Minimum and Maximum: The smallest and largest numbers in your list.
3. Find the Median (Q2): The middle number. If there is an even amount of numbers, average the two middle ones.
4. Find Q1: The median of the lower half of the numbers (everything to the left of the median).
5. Find Q3: The median of the upper half of the numbers (everything to the right of the median).

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Problem 1

Data: 11, 27, 20, 10, 13, 25, 18, 15, 5

Step 1: Order the data
5, 10, 11, 13, 15, 18, 20, 25, 27

Step 2: Find Min and Max
* Minimum: 5
* Maximum: 27

Step 3: Find the Median (Q2)
There are 9 numbers. The middle one is the 5th number.
5, 10, 11, 13, 15, 18, 20, 25, 27
* Q2: 15

Step 4: Find Q1 and Q3
Split the data into a lower half and an upper half around the median (15).
* Lower half: 5, 10, 11, 13
* Upper half: 18, 20, 25, 27

* Q1: The median of the lower half (average of 10 and 11).
$10 + 11 = 21$. $21 / 2 = 10.5$
* Q3: The median of the upper half (average of 20 and 25).
$20 + 25 = 45$. $45 / 2 = 22.5$

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Problem 2

Data: 44, 29, 35, 17, 28, 21, 12, 19

Step 1: Order the data
12, 17, 19, 21, 28, 29, 35, 44

Step 2: Find Min and Max
* Minimum: 12
* Maximum: 44

Step 3: Find the Median (Q2)
There are 8 numbers (an even amount). We take the average of the two middle numbers (the 4th and 5th numbers: 21 and 28).
$21 + 28 = 49$. $49 / 2 = 24.5$
* Q2: 24.5

Step 4: Find Q1 and Q3
Split the data into two halves. Since the median was calculated from the middle two, the lower half is the first 4 numbers, and the upper half is the last 4 numbers.
* Lower half: 12, 17, 19, 21
* Upper half: 28, 29, 35, 44

* Q1: The median of the lower half (average of 17 and 19).
$17 + 19 = 36$. $36 / 2 = 18$
* Q3: The median of the upper half (average of 29 and 35).
$29 + 35 = 64$. $64 / 2 = 32$

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Problem 3

Data: 51, 34, 26, 60, 52, 23, 49, 37, 59

Step 1: Order the data
23, 26, 34, 37, 49, 51, 52, 59, 60

Step 2: Find Min and Max
* Minimum: 23
* Maximum: 60

Step 3: Find the Median (Q2)
There are 9 numbers. The middle one is the 5th number.
23, 26, 34, 37, 49, 51, 52, 59, 60
* Q2: 49

Step 4: Find Q1 and Q3
Split the data around the median (49).
* Lower half: 23, 26, 34, 37
* Upper half: 51, 52, 59, 60

* Q1: The median of the lower half (average of 26 and 34).
$26 + 34 = 60$. $60 / 2 = 30$
* Q3: The median of the upper half (average of 52 and 59).
$52 + 59 = 111$. $111 / 2 = 55.5$

Final Answer:

1)
Minimum: 5
Maximum: 27
Q1: 10.5
Q2: 15
Q3: 22.5

2)
Minimum: 12
Maximum: 44
Q1: 18
Q2: 24.5
Q3: 32

3)
Minimum: 23
Maximum: 60
Q1: 30
Q2: 49
Q3: 55.5