Consider the following variables, what is the measurement scale of them? What type of graph display can be applied? What type of central tendency measures can be applied? Circle the right one(s). Phone numberCategorical; Quantitative(continual)Bar, Pie, Histogram, StemplotMode, Median, MeanNominal, Ordinal, Interval, RatioWeight of a professional boxer in poundCategorical; Quantitative(continual)Bar, Pie, Histogram, StemplotMode, Median, MeanNominal, Ordinal, Interval, RatioSqft of housesCategorical; Quantitative(continual)Bar, Pie, Histogram, StemplotMode, Median, MeanNominal, Ordinal, Interval, RatioStudents’ age(as number of year)Categorical; Quantitative(continual)Bar, Pie, Histogram, StemplotMode, Median, MeanNominal, Ordinal, Interval, RatioStudents’ age(as child, adolescent, adult)Categorical; Quantitative(continual)Bar, Pie, Histogram, StemplotMode, Median, MeanNominal, Ordinal, Interval, RatioThe IQ scoreCategorical; Quantitative(continual)Bar, Pie, Histogram, StemplotMode, Median, MeanNominal, Ordinal, Interval, Ratio **Measurement Scales, Graph Types, and Central Tendency Measures for Various Variables**In this section, we explore the measurement scales for different variables and determine the suitable graph types and measures of central tendency that can be applied. | **Variable** | **Measurement Scale** | **Graph Display** | **Central Tendency Measures** ||--------------------------------------|-------------------------------------------|------------------------------------------|--------------------------------|| Phone number | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean || Weight of a professional boxer (lb) | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean || Sqft of houses | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean || Students' age (as number of years) | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean || Students' age (as child, adolescent, adult) | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean || The IQ score | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |### Key Points:- **Categorical vs. Quantitative:** Variables can be categorical (e.g., phone number, student age categories) or quantitative, often referred to as continuous (e.g., weight, square footage, or IQ scores).- **Graph Types:** Different visualization methods are applicable, including bar charts, pie charts, histograms, and stemplots. The choice depends on the nature of the data.- **Central Tendency Measures:** Depending on the data, it may be appropriate to calculate mode, median, or mean to summarize the central point of the data distribution.This table provides a comprehensive view for educational purposes, explaining how to categorize and analyze different data types effectively.

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Consider the following variables, what is the measurement scale of them? What type of graph display can be applied? What type of central tendency measures can be applied? Circle the right one(s).

Phone number	Categorical; Quantitative(continual)	Bar, Pie, Histogram, Stemplot	Mode, Median, Mean
Nominal, Ordinal, Interval, Ratio
Weight of a professional boxer in pound	Categorical; Quantitative(continual)	Bar, Pie, Histogram, Stemplot	Mode, Median, Mean
Nominal, Ordinal, Interval, Ratio
Sqft of houses	Categorical; Quantitative(continual)	Bar, Pie, Histogram, Stemplot	Mode, Median, Mean
Nominal, Ordinal, Interval, Ratio
Students’ age (as number of year)	Categorical; Quantitative(continual)	Bar, Pie, Histogram, Stemplot	Mode, Median, Mean
Nominal, Ordinal, Interval, Ratio
Students’ age (as child, adolescent, adult)	Categorical; Quantitative(continual)	Bar, Pie, Histogram, Stemplot	Mode, Median, Mean
Nominal, Ordinal, Interval, Ratio
The IQ score	Categorical; Quantitative(continual)	Bar, Pie, Histogram, Stemplot	Mode, Median, Mean
Nominal, Ordinal, Interval, Ratio

**Measurement Scales, Graph Types, and Central Tendency Measures for Various Variables**

In this section, we explore the measurement scales for different variables and determine the suitable graph types and measures of central tendency that can be applied.

| **Variable** | **Measurement Scale** | **Graph Display** | **Central Tendency Measures** |
|--------------------------------------|-------------------------------------------|------------------------------------------|--------------------------------|
| Phone number | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |
| Weight of a professional boxer (lb) | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |
| Sqft of houses | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |
| Students' age (as number of years) | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |
| Students' age (as child, adolescent, adult) | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |
| The IQ score | Categorical; Quantitative (continuous) | Bar, Pie, Histogram, Stemplot | Mode, Median, Mean |

### Key Points:
- **Categorical vs. Quantitative:** Variables can be categorical (e.g., phone number, student age categories) or quantitative, often referred to as continuous (e.g., weight, square footage, or IQ scores).
- **Graph Types:** Different visualization methods are applicable, including bar charts, pie charts, histograms, and stemplots. The choice depends on the nature of the data.
- **Central Tendency Measures:** Depending on the data, it may be appropriate to calculate mode, median, or mean to summarize the central point of the data distribution.

This table provides a comprehensive view for educational purposes, explaining how to categorize and analyze different data types effectively.

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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