TOIN ONE (30 marks) a) Assume that you are a manager of a big organization that deals in goods and services and that you have a big team of human resource to work with Suggest and explain briefly some 4 ways in which statistics will be useful to you in everyday running of the organization. (4marks) b) Explain the differences between: (6marks) i. A sample and a population. ii. Inferential and Descriptive statistics iii. Skewness and Kurtosis

a) As a manager of a big organization, statistics can be useful in the following ways:<br /><br />1. **Performance Evaluation**: Statistics can be used to evaluate the performance of employees and teams. By analyzing data on productivity, efficiency, and other performance metrics, managers can identify areas where employees are excelling and areas where they may need improvement. This can help in making informed decisions about promotions, training, and other HR-related matters.<br /><br />2. **Market Analysis**: Statistics can be used to analyze market trends and consumer behavior. By analyzing data on sales, customer preferences, and other market-related metrics, managers can make informed decisions about product development, pricing, and marketing strategies.<br /><br />3. **Risk Management**: Statistics can be used to assess and manage risks within the organization. By analyzing data on past events, managers can identify potential risks and develop strategies to mitigate them. This can help in reducing the likelihood of unexpected events and minimizing their impact on the organization.<br /><br />4. **Decision Making**: Statistics can be used to make informed decisions about various aspects of the organization. By analyzing data on various metrics, managers can identify patterns and trends that can inform decision-making processes. This can help in making decisions that are based on data rather than intuition or assumptions.<br /><br />b) Differences between:<br /><br />i. **Sample and Population**: A sample is a subset of a population that is selected for analysis. A population is the entire group of individuals or items that is being studied. In other words, a sample is a smaller group of individuals or items that is selected from a larger population. For example, if a researcher wants to study the average height of all adults in a country, the population would be all adults in that country. If the researcher only studies a group of 1,000 adults, that group would be a sample.<br /><br />ii. **Inferential and Descriptive Statistics**: Descriptive statistics is the branch of statistics that deals with summarizing and organizing data. It provides basic information about the data, such as the mean, median, and mode. Inferential statistics, on the other hand, is the branch of statistics that deals with making inferences about a population based on a sample. It uses probability theory to make predictions about the population based on the sample data.<br /><br />iii. **Skewness and Kurtosis**: Skewness is a measure of the asymmetry of a distribution. It indicates the extent to which the data is skewed or lopsided. A distribution is said to be skewed if it is not symmetric. Kurtosis, on the other hand, is a measure of the "tailedness" of a distribution. It indicates the extent to which the data is concentrated in the tails of the distribution. A distribution is said to be leptokurtic if it has heavy tails and is concentrated in the center, and platykurtic if it has light tails and is spread out.