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.
![***Finding the First Quartile***
Calculate the first quartile (Q1) for the following dataset:
**Dataset:**
\[12, 14, 18, 32, 59, 82\]
**Steps to Find Q1:**
1. Arrange the data in ascending order (already done here).
2. Determine the position of the first quartile using the formula:
\[Q1 = \left(\frac{n + 1}{4}\right)^{th} \text{value}\]
where \( n \) is the number of data points.
3. If the position is a decimal, take the average of the values just above and below this position.
In this example:
1. \( n = 6 \)
2. \( Q1 = \left(\frac{6 + 1}{4}\right)^{th} \text{value} = \frac{7}{4} = 1.75^{th} \text{value} \)
\[ Q1 \] will lie between the \(1^{st}\) and \(2^{nd}\) values:
\[ Q1 = 12 + 0.75 \times (14 - 12) \]
\[ Q1 = 12 + 1.5 = 13.5 \]
Thus, the first quartile \( Q1 \) is approximately 13.5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb73ff27-6698-419e-8c3a-1f659f0b638e%2Fa38d2eda-de70-44a6-92e5-eea69fa382ee%2F7t8thf8_processed.jpeg&w=3840&q=75)
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