Air pollution control specialists in Southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours in the day. On July 15, the following levels of nitrogen dioxide were observed at different intervals from 6:00 AM. to 6:00 PM: Table 3.1 1089 528 257 2030 488 2081 384 200 522 1265 375 424 Compute the standard deviation and variance of nitrogen dioxide levels for the given data in above table. Compute the z-score for nitrogen dioxide levels 522, 1018.
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.
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Air pollution control specialists in Southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis.
The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours in the day. On July 15, the following levels of nitrogen dioxide were observed at different intervals from 6:00 AM. to 6:00 PM:
|
Table 3.1 |
||||||
|
1089 |
528 |
257 |
2030 |
488 |
2081 |
|
|
384 |
200 |
522 |
1265 |
375 |
424 |
- Compute the standard deviation and variance of nitrogen dioxide levels for the given data in above table.
- Compute the z-score for nitrogen dioxide levels 522, 1018.
- Create a box plot for consultation hours of the teachers. Which of the values, if any, are outliers? Show complete working of all calculations.
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