Sure! Let's break down the process of drawing a box plot for the dataset {19, 36, 23, 42, 21, 33, 23, 24, 36, 42, 23, 37, 37, 33, 17} step-by-step.
### Step 1: Organize the Data
First, we need to order the dataset in ascending order:
[tex]\[ 17, 19, 21, 23, 23, 23, 24, 33, 33, 36, 36, 37, 37, 42, 42 \][/tex]
### Step 2: Find the Five-Number Summary
The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
- Minimum: The smallest number in the dataset is 17.
- Q1 (First Quartile): This is the median of the first half of the dataset.
[tex]\[ Q1 = 23 \][/tex]
- Median: The central value of the dataset.
[tex]\[ \text{Median} = 33 \][/tex]
- Q3 (Third Quartile): This is the median of the second half of the dataset.
[tex]\[ Q3 = 36.5 \][/tex]
- Maximum: The largest number in the dataset is 42.
Therefore, the five-number summary is:
[tex]\[ (17, 23, 33, 36.5, 42) \][/tex]
### Step 3: Draw the Box Plot
Using the five-number summary, draw the plot:
1. Minimum (17): This is the left whisker end.
2. Q1 (23): The left edge of the box.
3. Median (33): The line inside the box.
4. Q3 (36.5): The right edge of the box.
5. Maximum (42): This is the right whisker end.
### Matching the Option
Given that the values are:
[tex]\[ 17, 23, 33, 36.5, 42 \][/tex]
Let's place the correct option:
- Option A: Incorrect
- Option B: Incorrect
- Option C: Correct
- Option D: Incorrect
Thus, the correct option to represent the box plot of the data {19, 36, 23, 42, 21, 33, 23, 24, 36, 42, 23, 37, 37, 33, 17} is:
Option C.
