Statistics and Data Analysis Challenge

What are the properties of a normal distribution?

• Always has a uniform distribution

• The properties of a normal distribution include symmetry, defined by mean and standard deviation, the Empirical Rule, total area under the curve equals 1, and asymptotic tails.

• Total area under the curve is greater than 1

• Mean and median are always equal to zero

How do you calculate the standard deviation of a dataset?

• Standard deviation is the sum of all data points divided by the number of points.

• Standard deviation is calculated by multiplying the mean by the number of data points.

• Standard deviation is calculated as the square root of the average of the squared differences from the mean.

• Standard deviation is the average of the data points without considering the mean.

What is the relationship between variance and standard deviation?

• Standard deviation and variance are unrelated concepts.

• Variance is the square root of standard deviation.

• Standard deviation is the square root of variance.

• Standard deviation is the variance squared.

Define the difference between population data and sample data.

• Population data is always smaller than sample data.

• Population data is a random selection from sample data.

• Sample data includes all members of a defined group.

• Population data includes all members of a defined group; sample data includes only a portion of that group.

What are dependent variables and how do they differ from independent variables?

• Dependent variables are always constant; independent variables vary.

• Independent variables are the outcomes measured in an experiment.

• Dependent variables are outcomes measured in an experiment; independent variables are factors manipulated to observe their effect.

• Dependent variables are manipulated to observe their effect.

List the measures of central tendency and explain each one.

• Sum, Count, Frequency

• Mean, Median, Mode

• Quartiles, Percentiles, Deviation

• Average, Range, Variance

What type of graph is best for displaying frequency distributions?

• Pie Chart

• Line Graph

• Histogram

• Bar Graph

How is a histogram different from a line graph?

• A histogram displays data points as dots, while a line graph uses bars.

• A histogram is used for categorical data, while a line graph is for numerical data.

• A histogram connects data points with lines, while a line graph uses bars to show frequency.

• A histogram shows frequency distribution, while a line graph shows trends over time.

What is a time series data and how is it used?

• Time series data consists of unrelated data points gathered from different sources.

• Time series data is a sequence of data points recorded at specific time intervals, used for analyzing trends and making forecasts.

• Time series data is only used for storing historical events without analysis.

• Time series data is a collection of random data points without any time component.

Explain what panel data is and provide an example.

• An example of panel data is a dataset containing annual income information for a group of individuals over a span of 10 years, where each individual's income is recorded each year.

• A dataset showing the monthly temperature of a city for one year.

• A list of book titles published each year by an author.

• A collection of images taken by a photographer over a decade.