what does the author achieve by mixing exact and approximate numbers in A contribution to Statistics?

Mixing exact and approximate numbers in "A contribution to Statistics" can serve several purposes for the author:

1. Enhancing credibility: By including both exact and approximate numbers, the author demonstrates their knowledge of the subject matter and suggests that they have carefully researched and analyzed the data. It gives an impression that the author has taken into account both the precise data available as well as the broader, approximate trends.

2. Providing context: Exact numbers can offer specific and precise information while approximate numbers can give a general sense of the magnitude or scale involved. By using both, the author can present a more comprehensive view of the topic, giving readers a better understanding of the overall context.

3. Simplicity and accessibility: Not all data might be readily available or easily expressed with exact figures. Approximate numbers can help simplify complex statistical concepts or large datasets, making them more accessible to a broader audience. They can also assist in conveying general trends or patterns.

4. Filling data gaps: In some cases, there might be missing or incomplete data. By using both exact and approximate numbers, the author can fill these gaps to provide a more comprehensive analysis. It allows for a more nuanced discussion, considering both the information that is precise and the information that is estimated.

5. Reflecting uncertainty: In certain statistical analyses, there may be inherent uncertainties or variations in measurements. Mixing exact and approximate numbers acknowledges this uncertainty, avoiding a false sense of precision and ensuring a more accurate representation of the data.

Overall, by utilizing a combination of exact and approximate numbers, the author can present a well-rounded and detailed analysis that considers both the specific details and the broader trends inherent in the data.