How do i interpret summary statistics and frequency tables?

Question

I need to know how to interpret summary statistics (for quantitative variables) and frequency tables (for categorical variables), but specifically for finding discrepancies in the data set.

For summary statistics, what do the mean, median, minimum, maximum, range, and standard deviation tell us about errors in the data set?

For frequency tables, how can I find find errors in the dataset from this when the frequency table just tells me how frequent each category is?

Thank you in advance.

Answer 1

Summary Statistics for Quantitative Variables

Here’s what each statistic of the summary statistics can tell you about potential errors:

1. Mean:
2. What it is: The average of all data points.
3. Detecting errors: Extremely high or low values (outliers) can skew the mean. Compare the mean to the median to identify possible outliers.
4. Median:
5. What it is: The middle value when data points are ordered.
6. Detecting errors: If the median is very different from the mean, this may indicate the presence of outliers or a skewed distribution.
7. Minimum and Maximum:
8. What they are: The smallest and largest values in the dataset.
9. Detecting errors: Check if the minimum and maximum values are within a plausible range. Values that are unreasonably high or low may indicate data entry errors. (E.g., for a data set consisting of ages of high school students, a minimum value of 10 might pose an issue)
10. Range:
11. What it is: The difference between the maximum and minimum values.
12. Detecting errors: An unusually large range may signal the presence of outliers or errors. (E.g., the range of ages of high school students shouldn't be a value like 20)
13. Standard Deviation:
14. What it is: A measure of the dispersion or spread of data points around the mean.
15. Detecting errors: A high standard deviation suggests a wide spread of values, which could include outliers. If the standard deviation is zero or very small, it might indicate that all values are the same or data recording issues.

Frequency Tables for Categorical Variables

Frequency tables summarize how often each category occurs in the dataset, which calls for different ways of detecting errors:

1. Unexpected Frequencies:
2. What to look for: Compare the frequencies of categories with your expectations or known benchmarks.
3. Detecting errors: If a category appears much more or less frequently than expected, it might indicate data entry errors or misclassification.
4. Uncommon or Unexpected Categories:
5. What to look for: Review the categories to ensure they are all valid and expected.
6. Detecting errors: Unexpected categories may indicate typos or incorrect coding. For example, “Male,” “Female,” and “Femle” might appear, where “Femle” is an error.
7. Missing Categories:
8. What to look for: Ensure all possible categories are represented.
9. Detecting errors: If a known category is missing, it could indicate data collection or entry issues.

The common theme is that prior/common knowledge of the dataset in question influences your expectations and thus the methods you use to find the errors. Hopefully this is helpful.