Give step-by-step solution with explanation and final answer:
The director of the Art Institute would like to present some data on the size of donations in this year
’
s annual report. He selects the following four categories to summarize donations: Friend of the Institute Silver Member Gold Member Platinum Member
(
$
2
5
to $
9
9
)
(
$
1
0
0
to $
2
4
9
)
(
$
2
5
0
to $
4
9
9
)
(
$
5
0
0
and above
)
To get a sense of what the data will look like, the director gives you a sample of donations measured at the interval level and asks you to apply the coding scheme. Create an ordinal
-
level variable for donations using the data below.
(
Hint: To get started, you first need to assign a numerical code to each category.
)
Interval Version
(
in $
)
Ordinal Version
2
5
1
5
0
7
5
4
5
0
1
0
0
7
5
0
9
0
1
7
5
2
5
0
5
0
Question:
Give step-by-step solution with explanation and final answer:
The director of the Art Institute would like to present some data on the size of donations in this year
’
s annual report. He selects the following four categories to summarize donations: Friend of the Institute Silver Member Gold Member Platinum Member
(
$
2
5
to $
9
9
)
(
$
1
0
0
to $
2
4
9
)
(
$
2
5
0
to $
4
9
9
)
(
$
5
0
0
and above
)
To get a sense of what the data will look like, the director gives you a sample of donations measured at the interval level and asks you to apply the coding scheme. Create an ordinal
-
level variable for donations using the data below.
(
Hint: To get started, you first need to assign a numerical code to each category.
)
Interval Version
(
in $
)
Ordinal Version
2
5
1
5
0
7
5
4
5
0
1
0
0
7
5
0
9
0
1
7
5
2
5
0
5
0
This is AI generated Response.
Asked by: Venky
Created at: 2025-09-22 06:30:06
Final Answer:
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# Step-by-Step Solution: Coding Donations into Ordinal Categories
## 1. Define the Categories and Codes
Assign numerical codes to the donation categories (lowest to highest):
| Category | Interval ($) | Ordinal Code |
|-----------------------------|------------------|--------------|
| Friend of the Institute | $25 – $99 | 1 |
| Silver Member | $100 – $249 | 2 |
| Gold Member | $250 – $499 | 3 |
| Platinum Member | $500 and above | 4 |
---
## 2. Donation Data (Interval Level)
List of sample donations:
25, 150, 75, 450, 100, 750, 90, 175, 250, 50
---
## 3. Assign Ordinal Codes
Go through each donation and assign the correct ordinal code:
| Donation ($) | Category | Ordinal Code |
|--------------|----------------------|--------------|
| 25 | Friend | 1 |
| 150 | Silver | 2 |
| 75 | Friend | 1 |
| 450 | Gold | 3 |
| 100 | Silver | 2 |
| 750 | Platinum | 4 |
| 90 | Friend | 1 |
| 175 | Silver | 2 |
| 250 | Gold | 3 |
| 50 | Friend | 1 |
---
## 4. Final Ordinal Level Data
The ordinal version, using the codes:
**Ordinal Version:**
1, 2, 1, 3, 2, 4, 1, 2, 3, 1
---
## 5. Explanation
- Each donation is matched to its category based on the value.
- The category is then replaced with the corresponding ordinal code.
- This coding transforms interval data into an ordinal variable suitable for summary statistics or further analysis.
---
## **Summary Table**
| Interval Version ($) | Ordinal Version (Code) |
|----------------------|------------------------|
| 25 | 1 |
| 150 | 2 |
| 75 | 1 |
| 450 | 3 |
| 100 | 2 |
| 750 | 4 |
| 90 | 1 |
| 175 | 2 |
| 250 | 3 |
| 50 | 1 |
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