Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were: Aptitude Score01 23 4 5 5 3 Frequency 3 4 The average (mean) aptitude score: The median aptitude score: 2. 3.
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.
![### Musical Aptitude Test Results Analysis
Each year, the students at a school undergo a musical aptitude test that assesses their musical skills on a scale from 0 (no musical aptitude) to 5 (high musical aptitude). The results for this year's test are as follows:
#### Aptitude Scores Distribution:
| Aptitude Score | Frequency |
|:--------------:|:---------:|
| 0 | 5 |
| 1 | 3 |
| 2 | 3 |
| 3 | 3 |
| 4 | 2 |
| 5 | 4 |
#### Statistical Analysis:
- **The average (mean) aptitude score:** [Answer to be filled in based on calculation]
- **The median aptitude score:** [Answer to be filled in based on calculation]
#### Calculation of the Average (Mean) Aptitude Score:
To calculate the average (mean) aptitude score, use the formula:
\[ \text{Average} = \frac{\sum (\text{Aptitude Score} \times \text{Frequency})}{\sum \text{Frequency}} \]
#### Calculation of the Median Aptitude Score:
To find the median aptitude score, list all scores in ascending order and find the middle value:
\[ \text{Median} = \text{middle value of the ordered data set} \]
This analysis helps in determining the overall musical aptitude levels of the students in the school for the given year.
For further understanding, teachers can guide students through these calculations, ensuring they gain hands-on experience with statistical analysis concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec37aac0-7d29-4e20-aa79-8267bb27a4fc%2F65b834f5-a3d0-4022-8de9-83a20eb62942%2F2ck3pur_processed.png&w=3840&q=75)
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