Exploring Averages in Statistics

What is the mode of the following set of numbers: 3, 7, 3, 2, 9?

• 2

• 7

• 3

• 9

In a dataset, if the mode is 5, what does that indicate about the data?

• The number 5 is the average of the dataset.

• The number 5 is the most frequently occurring value in the dataset.

• The number 5 appears only once in the dataset.

• The number 5 is the smallest value in the dataset.

How is the geometric mean calculated for a set of positive numbers?

• Geometric mean = (x1 + x2 + ... + xn) / n

• Geometric mean = (x1 * x2 * ... * xn) * n

• Geometric mean = (x1 - x2 - ... - xn)^(1/n)

• Geometric mean = (x1 * x2 * ... * xn)^(1/n)

What is a real-world application of the geometric mean?

• Calculating average growth rates in finance.

• Calculating average temperatures in meteorology.

• Estimating the mode in a statistical analysis.

• Finding the median of a data set.

If the mean of a dataset is significantly higher than the median, what does that suggest about the distribution?

• The distribution is negatively skewed.

• The distribution is uniform.

• The distribution is positively skewed.

• The distribution is normally distributed.

Provide an example where the mode is more informative than the mean.

• In the dataset [5, 5, 10, 15, 20], the mode (10) is more informative than the mean (11).

• In the dataset [10, 20, 30, 40, 50], the mode (20) is more informative than the mean (30).

• In the dataset [50, 50, 50, 50, 100], the mode (50) is more informative than the mean (50).

• In the dataset [1, 2, 2, 3, 4], the mode (3) is more informative than the mean (2.4).

What is the geometric mean of the numbers 4, 16, and 64?

• 32

• 24

• 8

• 16

In a survey, if the median income is $50,000, what can be inferred about the income distribution?

• The income distribution has no outliers.

• The income distribution is perfectly normal.

• The income distribution is likely skewed, with many earning below $50,000.

• Most people earn exactly $50,000.

How do you find the median in a dataset with an even number of values?

• Select the middle value directly from the dataset.

• Multiply the two middle values together.

• Average the two middle values after sorting the dataset.

• Sort the dataset in descending order and take the first value.

What is the difference between the mean and the median in a skewed distribution?

• The median is affected by extreme values, while the mean is not.

• The mean is pulled towards the tail, while the median remains at the center.

• Both the mean and median are pulled towards the center in a skewed distribution.

• The mean and median are always the same in a skewed distribution.