(source: congressional research service) (source: national safety council)
29. the following items appear on a physician’s intake form. identify the level of measurement of the data.
a. temperature
b. allergies
c. weight
d. pain level (scale of 0 to 10)
30. the following items appear on an employment application. identify the level of measurement of the data.
a. highest grade level completed
b. gender
c. year of college graduation
d. number of years at last job
■ extending concepts
31. writing what is an inherent zero? describe three examples of data sets that have inherent zeros and three that do not.
32. writing describe two examples of data sets for each of the four levels of measurement. justify your answer.

Question

(source: congressional research service) (source: national safety council)
29. the following items appear on a physician’s intake form. identify the level of measurement of the data.
  a. temperature
  b. allergies
  c. weight
  d. pain level (scale of 0 to 10)
30. the following items appear on an employment application. identify the level of measurement of the data.
  a. highest grade level completed
  b. gender
  c. year of college graduation
  d. number of years at last job
■ extending concepts
31. writing what is an inherent zero? describe three examples of data sets that have inherent zeros and three that do not.
32. writing describe two examples of data sets for each of the four levels of measurement. justify your answer.

Accepted Answer

### Question 29
#### Part a: Temperature
# Explanation:
## Step1: Recall level of measurement types (Nominal, Ordinal, Interval, Ratio).
## Step2: Temperature (e.g., in °C or °F) has no true zero (0°C doesn't mean no temperature), differences are meaningful, ratios are not. So it's Interval.
# Answer: Interval

#### Part b: Allergies
# Explanation:
## Step1: Allergies are categories (e.g., "peanuts", "pollen", "none").
## Step2: Categories with no order or magnitude, so Nominal.
# Answer: Nominal

#### Part c: Weight
# Explanation:
## Step1: Weight has a true zero (0 weight means absence of weight), ratios (e.g., 80kg is twice 40kg) are meaningful, differences too. So Ratio.
## Step2: Identify characteristics of Ratio level.
# Answer: Ratio

#### Part d: Pain level (scale of 0 to 10)
# Explanation:
## Step1: Pain level is ordered (0 < 1 <... < 10), but differences (e.g., 1 - 0 vs 5 - 4) may not be equal. No true zero (0 pain is a category, not absence of pain). So Ordinal.
## Step2: Analyze order and equal difference.
# Answer: Ordinal

### Question 30
#### Part a: Highest grade level completed
# Explanation:
## Step1: Grade levels (e.g., 9th, 12th, college) are ordered, differences (e.g., 12th - 9th vs college - 12th) not equal, no true zero. So Ordinal.
## Step2: Check order and equal interval.
# Answer: Ordinal

#### Part b: Gender
# Explanation:
## Step1: Gender is a category (male, female, non - binary), no order. So Nominal.
## Step2: Identify category with no order.
# Answer: Nominal

#### Part c: Year of college graduation
# Explanation:
## Step1: Years (e.g., 2020, 2021) have no true zero (year 0 doesn't mean no graduation), differences (2021 - 2020 = 1 year) are meaningful, ratios (2021/2020) not. So Interval.
## Step2: Analyze zero and difference.
# Answer: Interval

#### Part d: Number of years at last job
# Explanation:
## Step1: Number of years has a true zero (0 years means no time at job), ratios (e.g., 4 years is twice 2 years) are meaningful, differences too. So Ratio.
## Step2: Check true zero and ratio.
# Answer: Ratio

### Question 31
# Brief Explanations:
An inherent zero is a zero that represents the absence of the quantity being measured (e.g., 0 weight means no weight, 0 dollars means no money).

**Data sets with inherent zeros**:
1. Weight of objects (0 kg means no mass).
2. Number of children in a family (0 means no children).
3. Distance traveled (0 miles means no distance covered).

**Data sets without inherent zeros**:
1. Temperature in °C (0°C doesn't mean no temperature).
2. Year of birth (year 0 doesn't exist in the context of human birth, and 0 year has no meaning of "no birth").
3. IQ scores (0 IQ is not a meaningful measure of absence of intelligence, just a very low score).
# Answer: An inherent zero represents the absence of the measured quantity. Examples with inherent zeros: weight, number of children, distance. Examples without: temperature (°C), year of birth, IQ scores.

### Question 32
# Brief Explanations:
The four levels of measurement are Nominal, Ordinal, Interval, Ratio.

**Nominal**:
- Example 1: Types of pets (dog, cat, bird). Just categories, no order.
- Example 2: Car brands (Toyota, Ford, Honda). Categories with no ranking.

**Ordinal**:
- Example 1: Movie ratings (G, PG, PG - 13, R). Ordered, but differences (G to PG vs PG to PG - 13) not equal.
- Example 2: Letter grades (A, B, C, D, F). Ordered, but A - B vs B - C difference in quality not equal.

**Interval**:
- Example 1: Temperature in °F (32°F, 64°F). Differences (64 - 32 = 32°F) meaningful, no true zero (0°F doesn't mean no temperature).
- Example 2: Calendar years (2020, 2022). Differences (2022 - 2020 = 2 years) meaningful, no true zero (year 0 not meaningful in this context).

**Ratio**:
- Example 1: Height of people (150 cm, 300 cm). True zero (0 cm means no height), ratios (300/150 = 2) meaningful.
- Example 2: Number of books owned (0, 5, 10). True zero (0 books means no books), ratios (10/5 = 2) meaningful.
# Answer: Nominal: pet types, car brands. Ordinal: movie ratings, letter grades. Interval: temperature (°F), calendar years. Ratio: height, number of books. Justifications based on level characteristics.

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Question

Explanation:

Question 29

Part a: Temperature

Step1: Recall level of measurement types (Nominal, Ordinal, Interval, Ratio).

Step2: Temperature (e.g., in °C or °F) has no true zero (0°C doesn't mean no temperature), differences are meaningful, ratios are not. So it's Interval.

Step1: Allergies are categories (e.g., "peanuts", "pollen", "none").

Step2: Categories with no order or magnitude, so Nominal.

Step1: Weight has a true zero (0 weight means absence of weight), ratios (e.g., 80kg is twice 40kg) are meaningful, differences too. So Ratio.

Step2: Identify characteristics of Ratio level.

Answer:

Part b: Allergies