Final answer:
To compute measures of center (mean, median) and spread (standard deviation) for data on music downloads and video games, one must follow statistical methods that account for outliers and distribution. Such measures help describe the distribution and compare groups. Conclusions depend on sample representativeness and statistical assumption consistency.
Step-by-step explanation:
To address the student's question on computing the measures of center for music downloads and video games data among boys and girls, the mean and median must be calculated. The mean is the arithmetic average of the data, highly sensitive to outliers, whereas the median is the middle value that divides a dataset in half and is resistant to outliers. Differences in these measures of center can reveal the skewness or presence of outliers within data for both boys and girls.
As for the measures of spread, including the standard deviation, they quantify how data points are spread out around the mean. A high standard deviation indicates data points are spread out widely from the mean, while a low standard deviation suggests they are clustered closely. These are critical to understanding the variability and distribution of the data sets for boys and girls.
Valid conclusions from the collected data can be made if the data represents a random and representative sample, and the assumptions for statistical testing are properly met. Caution should be taken when inferring differences based on measures of centers and spreads, as confounding variables or sample size may affect validity.