The Federal Deposit Insurance Corporation (FDIC) was created in 1933 in response to the widespread bank failures during the Great Depression. The establishment of the FDIC aimed to restore public confidence in the nation's banking system by providing deposit insurance, which protects depositors' funds in the event of a bank failure. This federal insurance program significantly bolstered the stability of the banking sector and has been pivotal in ensuring that individuals can trust banks with their savings. The establishment of the FDIC marked a significant shift in banking regulation, reflecting the need for stronger safeguards against financial crises.

The statistical method used for making predictions based on past data trends is indeed referred to as predictive analysis. This approach focuses on using historical data to identify patterns and trends that can inform future outcomes. By analyzing past behaviors and trends, predictive analysis enables analysts to forecast future events or trends, which is highly valuable in various fields such as finance, marketing, and healthcare. Predictive analysis often involves applying techniques such as regression analysis, machine learning, and time series analysis to create models that can predict future values or behaviors based on previous data. This predictive capability is essential for decision-making and strategic planning. The other options represent different aspects of statistics: - Descriptive statistics involves summarizing and describing the characteristics of a dataset but does not focus on making predictions. - Sample analysis pertains to evaluating a subset of a population to infer characteristics about the whole but again does not inherently predict future trends. - Inferential statistics is concerned with making generalizations or inferences about a population based on a sample but does not specialize in prediction as its primary goal. Its primary focus is on hypothesis testing and estimating population parameters. By understanding these distinctions, it's clear why predictive analysis stands out as the appropriate method for making predictions based on historical data trends.

The mode of a set of numbers is defined as the value that appears most frequently. In the given amounts—$850, $885, $910, $825, $800, $900, $925—each number appears only once. Since there are no repeated values in this dataset, there isn't a number that occurs more often than any other. When evaluating the data, we see that while there are multiple unique values, none meet the criteria to be considered the mode, which means that the dataset lacks a mode. Therefore, stating that there is no mode accurately reflects the absence of any repeating values in the provided amounts.

The federal agency established to insure bank deposits is the Federal Deposit Insurance Corporation (FDIC). Created in 1933 during the Great Depression, the FDIC aims to maintain public confidence in the U.S. financial system by protecting depositors against the loss of their insured deposits if an FDIC-insured bank or savings institution fails. This insurance protects individual accounts up to a certain limit, which provides a safety net for depositors, thereby helping to prevent bank runs and stabilizing the banking system. Other agencies mentioned, such as the Federal Housing Administration (FHA), Federal Housing Finance Agency (FHFA), and Federal National Mortgage Association (FNMA), have different roles primarily focused on housing finance rather than directly insuring bank deposits. FHA provides mortgage insurance on loans made by approved lenders, while FHFA regulates and oversees government-sponsored enterprises like Fannie Mae (FNMA), which focuses on increasing the availability of mortgage financing.