Statistical Analysis Challenge

What is the mean of the following data set: 2, 4, 6, 8, 10?

• 6

• 8

• 4

• 10

Define the term 'standard deviation'.

• Standard deviation is the average of a set of values.

• Standard deviation is a measure of the amount of variation or dispersion in a set of values.

• Standard deviation measures the central tendency of a dataset.

• Standard deviation is a fixed value that does not change.

What is the purpose of a histogram in statistical analysis?

• To perform hypothesis testing on categorical data.

• To determine the correlation between two variables.

• To calculate the mean of a dataset.

• To visualize the distribution of numerical data.

Explain the difference between a population and a sample.

• A population is always smaller than a sample.

• A population is the entire group of interest, whereas a sample is a smaller, representative subset of that population.

• A sample includes every member of the population.

• A population is a random selection from a sample.

How do you calculate the median of a data set?

• Add all values and divide by the number of values.

• Count the total number of values without arranging them.

• Select the highest value in the data set.

• Arrange data in order; find middle value or average of two middle values.

What is a normal distribution?

• A normal distribution is a uniform distribution with equal probabilities across all values.

• A normal distribution is a skewed probability distribution with no defined mean.

• A normal distribution is a discrete distribution that only applies to whole numbers.

• A normal distribution is a symmetric probability distribution characterized by a bell-shaped curve, defined by its mean and standard deviation.

What does a p-value represent in hypothesis testing?

• A p-value represents the probability of obtaining test results at least as extreme as the observed results, given that the null hypothesis is true.

• A p-value indicates the strength of the null hypothesis.

• A p-value shows the probability of the alternative hypothesis being true.

• A p-value measures the effect size of the observed results.

Describe the concept of correlation and its significance.

• Correlation is only relevant in qualitative research.

• Correlation is a measure of the average of two variables.

• Correlation is a statistical measure of the relationship between two variables, significant for understanding patterns and making predictions.

• Correlation indicates that one variable causes changes in another.

What is the difference between descriptive and inferential statistics?

• Descriptive statistics summarize data; inferential statistics make predictions about a population based on a sample.

• Descriptive statistics are used for qualitative data; inferential statistics are used for quantitative data.

• Descriptive statistics predict future trends; inferential statistics summarize data.

• Descriptive statistics analyze data; inferential statistics collect data.

How can outliers affect the mean of a data set?

• Outliers always increase the mean value.

• Outliers only affect the median, not the mean.

• Outliers can distort the mean, making it unrepresentative of the data set.

• Outliers have no effect on the mean.