Identify numerical data irregularities that could occur and explain how these would be resolved using established procedures.

1. Outliers: Outliers are data points that are significantly different from the rest of the data. These can skew the results of analysis and should be identified and removed. One way to identify outliers is by using statistical methods such as the Z-score or the IQR (Interquartile Range) method. Once outliers are identified, they can be removed from the dataset or replaced with a more appropriate value (e.g. the mean or median).

2. Missing data: Missing data can occur due to various reasons such as data entry errors or non-response. To resolve missing data, one can use techniques such as imputation, where missing values are replaced with estimated values based on the rest of the data. Imputation methods include mean imputation, median imputation, or regression imputation.

3. Data duplication: Data duplication can occur when the same data point is recorded multiple times in a dataset. This can lead to inflated results and should be identified and removed. One way to identify data duplication is by using unique identifiers or by comparing data points for similarity. Once identified, duplicated data points can be removed from the dataset.

4. Data entry errors: Data entry errors can occur when incorrect values are entered into the dataset. To resolve data entry errors, one can perform data validation checks to ensure that the data entered meets certain criteria. Additionally, data cleaning techniques such as removing special characters or correcting typos can help resolve data entry errors.

5. Skewed data distribution: Skewed data distribution can occur when the data is not normally distributed. This can affect the results of analysis and should be addressed. One way to resolve skewed data distribution is by transforming the data using techniques such as log transformation or Box-Cox transformation to make the data more normally distributed.

Numerical Data Irregularities

- Outliers: Extreme values that deviate significantly from the rest of the data.
- Missing values: Data points that are not available for some reason.
- Errors: Incorrect numerical values due to data entry mistakes or other issues.
- Inconsistent units: Data points using different units of measurement.

Resolution Procedures

Outliers:

- Examine the data: Determine if the outlier is a valid data point or an anomaly.
- Investigate the source: Check for data entry errors or other factors that may have caused the outlier.
- Remove the outlier: If the outlier is confirmed to be invalid or not representative of the data, it should be removed.

Missing Values:

- Impute the missing value: Estimate the missing value using statistical techniques, such as mean, median, or regression analysis.
- Exclude the observation: Remove the observation from the analysis if the missing value cannot be imputed with confidence.

Errors:

- Verify the data source: Check the original source of the data to identify and correct any errors.
- Use data validation tools: Employ software or manual checks to identify and correct erroneous data.
- Re-enter the data: If possible, manually re-enter the data to eliminate errors from the original source.

Inconsistent Units:

- Convert to a common unit: Convert all data points to a common unit of measurement.
- Recalculate the results: Perform calculations again using the consistent units to ensure accurate results.

Additional Best Practices:

- Use data visualization: Create graphs and charts to identify outliers and other irregularities visually.
- Establish data quality standards: Define acceptable ranges and limits for numerical data to prevent errors and inconsistencies.
- Document data transformations: Keep a record of any data transformations or manipulations performed to ensure transparency and reproducibility.