For the following data find the three quartiles and the IQR, then any outliers. 6, 12, 14, 15, 18, 22, 29, 40, 50 Q1 = Q2 = Q3 = IQR = Interval for Outliers: Outliers: (State “none” if there are no outliers. Make sure you determine the interval for outliers.)
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.
For the following data find the three
6, 12, 14, 15, 18, 22, 29, 40, 50
Q1 =
Q2
=
Q3
=
IQR =
Interval for Outliers:
Outliers:
(State “none” if there are no outliers. Make sure you determine the interval for outliers.)
- The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
6 12 14 15 18 22 29 40 50
So, the bottom half is
6 12 14 15
The median of these numbers is 13.
Q1 = 13
- The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
6 12 14 15 18 22 29 40 50
So, the upper half is
22 29 40 50
The median of these numbers is 34.5.
Q3 = 34.5
The interquartile range is the difference between the third and first quartiles.
The third quartile is 34.5.
The first quartile is 13.
The interquartile range (IQR)= 34.5 - 13 = 21.5.
- Outlier :
An outlier is a value in a sample that too extreme. Such definition begs to be more precise: What do we mean for being "too extreme"? There are diverse interpretations of this notion of being too extreme. One common rule to decide whether a value in a sample is too extreme is whether or not the value is beyond 1.5 times the Interquartile Range from the first or third quartiles .
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