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Comparing means is a fundamental aspect of descriptive statistics. In this exercise, we are tasked with comparing two sets of mean IQ scores. The mean, or average, provides a central value for a data set. To find the mean, sum up all the values in a group and divide by the number of values in that group.

In practice, once you have calculated the means of the firstborn and youngest children’s IQs, you look at the difference between these two averages. If the mean IQ of firstborns is greater than that of the youngest children, you could initially conclude that firstborns are 'smarter'. However, only comparing the means doesn’t tell the whole story. You may need more statistical tests to determine the significance of the difference.

Random sampling refers to selecting a subset of individuals from a population where each individual has an equal chance of being chosen. This method ensures that the sample represents the broader population and is free from bias.

In the given exercise, selecting 100 households randomly helps to ensure that the IQ scores measured are representative of the entire population of households with at least two children. This method is crucial because it minimizes the likelihood that any particular subset of the population is overrepresented in the sample, leading to more reliable and generalizable results.

IQ, or Intelligence Quotient, is a measure of a person’s intellectual abilities in relation to others. IQ tests are designed to assess a variety of cognitive abilities such as memory, reasoning, and problem-solving.

In our exercise, measuring IQ for both firstborn and youngest children provides an opportunity to compare cognitive abilities across age and birth order within households. It’s important to note that while IQ can give insights into a child’s cognitive abilities, it is just one of many factors that contribute to a person’s intelligence.

Data analysis involves systematically applying statistical techniques to describe and interpret data. In the context of our exercise, calculating the mean, comparing these means, and interpreting the results are all parts of data analysis.

While the exercise focuses on basic comparison through mean calculations, deeper data analysis could involve examining the distribution of IQ scores, checking for any patterns or anomalies, and evaluating the statistical significance of observed differences. Such analysis often employs additional statistical tools like t-tests or ANOVA to strengthen conclusions drawn from data.