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Draw a box plot for the following data set:
[tex]\[ \{19, 36, 23, 42, 21, 33, 23, 24, 36, 42, 23, 37, 37, 33, 17\} \][/tex]

A.
[tex]\[ 15 \quad 20 \quad 25 \quad 30 \quad 35 \quad 40 \quad 45 \][/tex]

B.
[tex]\[ 15 \quad 20 \quad 25 \quad 30 \quad 35 \quad 40 \quad 45 \][/tex]

C.
[tex]\[ 15 \quad 20 \quad 25 \quad 30 \quad 35 \quad 40 \quad 45 \][/tex]

D.
[tex]\[ 15 \quad 20 \quad 25 \quad 30 \quad 35 \quad 40 \quad 45 \][/tex]

Sagot :

GinnyAnsweridn
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.
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