4) The heights (in inches) of ten different trees in a park were recorded as: $$ 50,55,60,45,52,48,62,58,54,59 $$ a) Identify the 5-number summary for this data. Minimum: Q1: Median: b) What is the interquartile range? c) Construct a box plot for the data.

Question

UpStudy AI · Accepted Answer

To solve the problem, we will follow these steps:

### Step 1: Organize the Data
First, we need to sort the heights of the trees in ascending order:
$$ 45, 48, 50, 52, 54, 55, 58, 59, 60, 62 $$

### Step 2: Calculate the 5-Number Summary
The 5-number summary consists of the following:
1. Minimum
2. First Quartile (Q1)
3. Median
4. Third Quartile (Q3)
5. Maximum

#### a) Identify the 5-number summary
1. **Minimum**: The smallest value in the dataset.
   $$
   \text{Minimum} = 45
   $$

2. **Median**: The middle value of the dataset. Since there are 10 values (even number), the median is the average of the 5th and 6th values.
   $$
   \text{Median} = \frac{54 + 55}{2} = 54.5
   $$

3. **First Quartile (Q1)**: The median of the first half of the data (the first 5 values).
   $$
   Q1 = \text{Median of } (45, 48, 50, 52, 54) = 50
   $$

4. **Third Quartile (Q3)**: The median of the second half of the data (the last 5 values).
   $$
   Q3 = \text{Median of } (55, 58, 59, 60, 62) = 59
   $$

5. **Maximum**: The largest value in the dataset.
   $$
   \text{Maximum} = 62
   $$

Thus, the 5-number summary is:
- Minimum: 45
- Q1: 50
- Median: 54.5
- Q3: 59
- Maximum: 62

### Step 3: Calculate the Interquartile Range (IQR)
The interquartile range is calculated as:
$$
\text{IQR} = Q3 - Q1 = 59 - 50 = 9
$$

### Step 4: Construct a Box Plot
To construct a box plot, we will use the 5-number summary:
- Minimum: 45
- Q1: 50
- Median: 54.5
- Q3: 59
- Maximum: 62

The box plot will have:
- A box from Q1 (50) to Q3 (59).
- A line at the median (54.5).
- Whiskers extending from the minimum (45) to Q1 and from Q3 to the maximum (62).

Now, I will create the box plot based on the calculated values.

### Box Plot Creation
Let's proceed to create the box plot.

Since I cannot create visual plots directly, I will provide the necessary data for you to create a box plot using any graphing tool or software.

- **Box Plot Data**:
  - Minimum: 45
  - Q1: 50
  - Median: 54.5
  - Q3: 59
  - Maximum: 62

You can use this data to create a box plot in software like Excel, Google Sheets, or any statistical software.

### Summary of Results
- **5-Number Summary**: Minimum: 45, Q1: 50, Median: 54.5, Q3: 59, Maximum: 62
- **Interquartile Range (IQR)**: 9
- **Box Plot**: Use the provided 5-number summary to create the box plot.
- **5-Number Summary**: - Minimum: 45 - Q1: 50 - Median: 54.5 - Q3: 59 - Maximum: 62 - **Interquartile Range (IQR)**: 9 - **Box Plot**: Use the 5-number summary to create the box plot.

The heights (in inches) of ten different trees in a park were recorded as:

a) Identify the 5-number summary for this data.
Minimum: Q1: Median:
b) What is the interquartile range?
c) Construct a box plot for the data.

Upstudy AI Solution

Answer

Solution

Step 1: Organize the Data

Step 2: Calculate the 5-Number Summary

a) Identify the 5-number summary

Step 3: Calculate the Interquartile Range (IQR)

Step 4: Construct a Box Plot

Box Plot Creation

Summary of Results

Beyond the Answer

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The heights (in inches) of ten different trees in a park were recorded as: a) Identify the 5-number summary for this data. Minimum: Q1: Median: b) What is the interquartile range? c) Construct a box plot for the data.