Stats & Probability Challenge

What is the mean of the following data set: 5, 8, 12, 15, 20?

• 10

• 18

• 25

• 12

Define the term 'standard deviation' in statistics.

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

• Standard deviation is the range of values in a dataset.

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

• Standard deviation measures the central tendency of a dataset.

If a data set has a mode of 10, what does this indicate?

• The data set has a mode of 20

• The data set has the number 10 occurring most frequently.

• The data set has no other values besides 10

• The data set has a mode of 5

Explain the difference between range and interquartile range.

• Range is the overall spread of the data, while interquartile range focuses on the middle 50% of the data, making it more robust to outliers.

• Range is calculated by subtracting the first quartile from the third quartile.

• Interquartile range includes the maximum and minimum values of the data.

• Range is the same as interquartile range.

Given a box plot, how can you determine the median of the data?

• Calculate the average of the data points in the box plot.

• Look for the highest value in the box plot.

• Locate the line within the box plot that represents the median.

• Count the number of data points in the box plot.

What is the purpose of using a histogram in data analysis?

• Histograms are used to show the relationship between two variables in a dataset.

• Histograms are used to display only the maximum value in a dataset.

• Histograms are used to identify outliers in a dataset.

• Histograms are used to visually represent the distribution of a dataset by grouping data into intervals and displaying the frequency of occurrences within each interval.

Calculate the variance of the data set: 3, 6, 9, 12, 15.

• 20

• 30

• 18

• 24

Interpret the correlation coefficient value of -0.75.

• Strong negative linear relationship

• Moderate positive linear relationship

• No relationship

• Weak positive linear relationship

Describe the concept of probability in simple terms.

• Probability is the likelihood of an event happening multiplied by the total number of possible outcomes

• Probability is the certainty of an event happening

• Probability is the chance of an event happening divided by the total number of possible outcomes.

• Probability is the total number of possible outcomes

If two events are independent, what is the probability of both events occurring?

• P(A) - P(B)

• P(A) * P(B)

• P(A) / P(B)

• P(A) + P(B)