the five-number summary, and (b) draw a box-and-whisker plot of the data. 3 8 8 4 1 9 8 7 9 4 9 3 1 6 1 9 8 7 7 9
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.
In descriptive statistic for non-grouped data, there is five important number that helps us to understand data behavior, they are minimum and maximum value, and first, second and third quartiles.
From smallest to largest we have:
| X |
| 1 |
| 1 |
| 1 |
| 3 |
| 3 |
| 4 |
| 4 |
| 6 |
| 7 |
| 7 |
| 7 |
| 8 |
| 8 |
| 8 |
| 8 |
| 9 |
| 9 |
| 9 |
| 9 |
| 9 |
and is obtained by calculating the median of the lower half and upper half respectively.
The median of the lower half of data set that has even number of observations is obtained by the formula , where (n) is the number of observations.
The median of the upper half of data set that has odd number of observations is obtained by the formula , where (n) is the number of observations.
The median of the data set that has even number of observations is obtained by the formula , where (n) is the number of observations.
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