Definition
Sample size refers to the number of units or respondents selected for inclusion in a study. Representativeness means that this subset accurately reflects the characteristics of the total population.

Introduction
Selecting the right sample size is both an art and a science. Too small, and the results lack reliability; too large, and resources are wasted. Representativeness ensures that findings can be generalized beyond the sample itself.

Explanation
Determining sample size involves balancing statistical confidence with practicality. Factors include population size, desired confidence level (usually 95%), margin of error, and variability within the population. The greater the variability, the larger the sample required.

Mathematically, researchers often use formulas like:
n = (Z² × p × q) / e²
where Z = confidence level, p = estimated proportion, q = 1 – p, and e = margin of error.

However, beyond numbers, representativeness is crucial. A 1,000-person survey about political attitudes must proportionally include various age groups, genders, and socioeconomic classes. Sampling bias occurs when certain segments are over- or under-represented, skewing conclusions.

Key Takeaways
Statistical accuracy depends more on representativeness than on sheer size. A small, well-chosen sample is better than a large, biased one.

Real-World Case
During national elections, polling agencies like Ipsos use carefully calibrated representative samples to predict results with remarkable accuracy, even though they survey only a fraction of the electorate.
Reference: https://www.ipsos.com