Measures of Central Tendency and Outliers

The video tutorial explains how to determine the best representation of the center of a data set when extreme outliers are present. It begins by calculating the mean and median of a simple data set and then introduces an extreme outlier to observe its effect. The tutorial demonstrates that while the mean is significantly affected by outliers, the median remains relatively stable, making it a better representation of the data set's center in such cases.

What is the main challenge when dealing with extreme outliers in a data set?

• They increase the number of calculations needed.

• They are difficult to identify.

• They can skew the representation of the data's center.

• They make the data set larger.

How do you calculate the mean of a data set?

• By adding all numbers and dividing by the count of numbers.

• By finding the middle number.

• By identifying the most frequent number.

• By subtracting the smallest number from the largest.

What is the median of the data set [3, 5, 7]?

• 6

• 7

• 5

• 3

What happens to the mean when an extreme outlier is added to a data set?

• It increases significantly.

• It remains the same.

• It decreases slightly.

• It becomes zero.

What is the new mean of the data set [3, 5, 7, 105]?

• 50

• 30

• 15

• 5

How is the median affected by the addition of an extreme outlier?

• It becomes the outlier.

• It remains relatively stable.

• It changes drastically.

• It doubles.

What is the new median of the data set [3, 5, 7, 105]?

• 6

• 5

• 7

• 105

Why is the median a better representation of the data set with outliers?

• It is the largest number.

• It always equals the mean.

• It is less affected by extreme values.

• It is easier to calculate.

Which measure of central tendency is more robust to outliers?

• Mode

• Mean

• Range

• Median

In the presence of extreme outliers, which measure should be used to represent the center of the data?

• Median

• Mean

• Mode

• Standard Deviation