What is the arithmetic mean of this data set? mean = 37 What is the median of this data set? median = 37.8 What is the mode of this data set? mode = 50.4
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.
The following refer to the following data set:
| 50.4 | 47.5 | 50.4 | 23.4 | 33.7 |
| 50.4 | 39.2 | 36.4 | 16.3 | 21.8 |
What is the arithmetic mean of this data set?
What is the median of this data set?
median = 37.8
What is the
mode = 50.4
Given data,
| 50.4 | 47.5 | 50.4 | 23.4 | 33.7 | 50.4 | 39.2 | 36.4 | 16.3 | 21.8 |
Number of elements in the data set n = 10
Rearranging the given data in ascending order
| 16.3 | 21.8 | 23.4 | 33.7 | 36.4 | 39.2 | 47.5 | 50.4 | 50.4 | 50.4 |
Mean of the data set= Sum of the elements in data set/ Number of element in data set
Sum of elements in data set = 16.3+21.8+23.4+33.7+36.4+39.2+47.5+50.4+50.4+50.4
= 370
Mean of the data set= 370/10
Mean of the data set= 37
Median of the data set= ((n+1)/2)th value in ascending order of data if n is odd
= Average of (n/2)th + ((n/2)+1)th value in ascending order of data if n is even
Here, n = 10
Hence median = average of 5th and 6th value in the ascending ordered data
Median = (36.4+39.2)/2
= 75.6/2
= 37.8
Median of the data set = 37.8
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