**Analyzing Singer Heights through One-Way ANOVA**This educational activity explores the relationship between the type of singer and their height using a statistical method called One-Way ANOVA. The data presented originate from the DASL (The Data and Story Library) database, specifically focusing on the heights (in inches) of different types of singers.**Graph Explanation:**The scatter plot visually presents the height distributions across four categories of singers: Soprano, Alto, Tenor, and Bass. Each category is represented by differently colored dots:- **Soprano**: Blue- **Alto**: Orange- **Tenor**: Gray- **Bass**: YellowThe y-axis denotes height in inches, ranging from 55 to 80 inches. The plot shows variability in height within each singing category, helping assess whether these differences are statistically significant.**ANOVA Summary Table:**The summary table lists statistical details for each singer group:- **Soprano**: - Count: 36 - Sum of Heights: 2313 - Average Height: 64.25 inches - Variance: 3.5071- **Alto**: - Count: 35 - Sum of Heights: 2271 - Average Height: 64.885714 inches - Variance: 7.8101- **Tenor**: - Count: 20 - Sum of Heights: 1383 - Average Height: 69.15 inches - Variance: 10.3447- **Bass**: - Count: 39 - Sum of Heights: 2758 - Average Height: 70.717949 inches - Variance: 5.5762**ANOVA Statistical Output:**- **Source of Variation**: - **Between Groups**: - Sum of Squares (SS): 1058.5289 - Degrees of Freedom (df): 3 - Mean Square (MS): 352.84298 - F-value: 55.800134 - P-value: 5.1E-23 (significant at conventional levels) - F critical (F crit): 2.67652 - **Within Groups**: - Sum of Squares **SINGERS***Choose the BEST endings for the following explanations.*1. The between-samples variance would be a measure of the variation in - [Choose] - average heights of singers in the same group. - heights of singers in the same group. - heights of singers across different groups. - average heights of singers across different groups.2. The within-samples variance would a measure of the variation in - [Choose]*Note: The dropdown menu currently shows the same options for both questions but only details for the first question are visible. The task involves selecting the most appropriate option for both instances to understand the variance in statistical terms as applied to singers.*

Name: **Analyzing Singer Heights through One-Way ANOVA**This educational ac
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Description: **Analyzing Singer Heights through One-Way ANOVA**This educational activity explores the relationship between the type of singer and their height using a statistical method called One-Way ANOVA. The data presented originate from the DASL (The Data a

Introduction: The ANOVA or analysis of variance is a parametric method of hypothesis testing,…

Math

Statistics

Choose the BEST endings for the following explanations. The between-samples variance v [ Choose ] average heights of singers in the same group. heights of singers in the same group. heights of singers across different groups. average heights of singers across different groups. would be a measure of the variation in The within-samples variance would a measure of the variation in

Choose the BEST endings for the following explanations. The between-samples variance v [ Choose ] average heights of singers in the same group. heights of singers in the same group. heights of singers across different groups. average heights of singers across different groups. would be a measure of the variation in The within-samples variance would a measure of the variation in

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

**Analyzing Singer Heights through One-Way ANOVA**

This educational activity explores the relationship between the type of singer and their height using a statistical method called One-Way ANOVA. The data presented originate from the DASL (The Data and Story Library) database, specifically focusing on the heights (in inches) of different types of singers.

**Graph Explanation:**

The scatter plot visually presents the height distributions across four categories of singers: Soprano, Alto, Tenor, and Bass. Each category is represented by differently colored dots:
- **Soprano**: Blue
- **Alto**: Orange
- **Tenor**: Gray
- **Bass**: Yellow

The y-axis denotes height in inches, ranging from 55 to 80 inches. The plot shows variability in height within each singing category, helping assess whether these differences are statistically significant.

**ANOVA Summary Table:**

The summary table lists statistical details for each singer group:

- **Soprano**:
- Count: 36
- Sum of Heights: 2313
- Average Height: 64.25 inches
- Variance: 3.5071

- **Alto**:
- Count: 35
- Sum of Heights: 2271
- Average Height: 64.885714 inches
- Variance: 7.8101

- **Tenor**:
- Count: 20
- Sum of Heights: 1383
- Average Height: 69.15 inches
- Variance: 10.3447

- **Bass**:
- Count: 39
- Sum of Heights: 2758
- Average Height: 70.717949 inches
- Variance: 5.5762

**ANOVA Statistical Output:**

- **Source of Variation**:
- **Between Groups**:
- Sum of Squares (SS): 1058.5289
- Degrees of Freedom (df): 3
- Mean Square (MS): 352.84298
- F-value: 55.800134
- P-value: 5.1E-23 (significant at conventional levels)
- F critical (F crit): 2.67652

- **Within Groups**:
- Sum of Squares

**SINGERS**

*Choose the BEST endings for the following explanations.*

1. The between-samples variance would be a measure of the variation in
- [Choose]
- average heights of singers in the same group.
- heights of singers in the same group.
- heights of singers across different groups.
- average heights of singers across different groups.

2. The within-samples variance would a measure of the variation in
- [Choose]

*Note: The dropdown menu currently shows the same options for both questions but only details for the first question are visible. The task involves selecting the most appropriate option for both instances to understand the variance in statistical terms as applied to singers.*

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