Answer
See expalantion
Work Step by Step
**a. Car Colors on a High‐Income Street**
- **Appropriate Measure:** **Mode**
- **Why:** Colors are nominal categories (names with no numerical ordering), so only the mode—the most frequently observed category—can meaningfully summarize the “central” tendency.
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**b. Helping Behavior Rated on a 1–5 Scale**
- **Appropriate Measure:** **Median**
- **Why:** The ratings are ordinal; while the numbers are ordered, the differences between them aren’t necessarily equal. The median, which gives the middle response, is best for ordinal data. (The mode could also be mentioned, but the median better captures a “typical” rating when order matters.)
The mode is also appropriate.
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**c. Household Income (Grouped into Open-Ended Categories)**
- **Appropriate Measure:** **Median**
- **Why:** Income data tend to be skewed, and when one of the groups (here, “$100,001 and more”) is open-ended, calculating a mean is problematic. The median is less affected by skew and doesn’t require knowing exact midpoints for an open-ended category.
The mode is also appropriate.
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**d. Per Capita Income (Grouped into Closed Categories)**
- **Appropriate Measure:** **Median** and **mode**
- **Why:** The distribution is often skewed.
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**e. First Admissions to a Mental Hospital Classified by Disorder**
- **Appropriate Measure:** **Mode**
- **Why:** The disorders are nominal categories (names of conditions with no inherent numeric order). Only the mode—the most common category—can appropriately represent the central tendency.
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**f. Arithmetic Test Scores**
- **Appropriate Measure:** **Mean**
- **Why:** Test scores are interval data. Even though most scores fall within 70–79 and a few lie above or below, the mean incorporates all values and is commonly used for test performance when the distribution isn’t heavily skewed by outliers. (In many cases, the median might also be similar, but the mean is the conventional summary statistic for test scores.)
