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.
![**Problem: Find the Third Quartile**
Given the data set: 15, 3, 4, 6, 8, 10, 20
Steps to find the third quartile (Q3):
1. **Arrange the data in ascending order.**
2. **Determine the position of Q3 using the formula:**
\[ Q3 = \frac{3(n + 1)}{4} \]
where \( n \) is the number of data points.
3. **Identify and interpret Q3 from the sorted data set.**
Example Solution:
1. **Arrange the data in ascending order:** 3, 4, 6, 8, 10, 15, 20
2. **Number of data points (n):** \( 7 \)
3. **Determine the position of Q3:**
\[ Q3 = \frac{3(7 + 1)}{4} = \frac{3 \times 8}{4} = \frac{24}{4} = 6 \]
So, the position of Q3 is the 6th value in the sorted data set.
4. **Interpret Q3:** The 6th value in the sorted data set is 15.
Therefore, the third quartile (Q3) is 15.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb73ff27-6698-419e-8c3a-1f659f0b638e%2F0052d2c4-d61e-41f9-8ced-8337fecdd02b%2Fbldwugt_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
